SecProbe.io

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Faegre Drinker Biddle & Reath LLP

One Logan Square, Suite 2000

Philadelphia, Pennsylvania 19103

www.faegredrinker.com

June 29, 2022

Via EDGAR Transmission

Securities and Exchange Commission

100 F Street, N.E.

Washington, D.C. 20549

Attention: Michael A. Rosenberg

 Re: Constitution Capital Private Markets Fund, LLC

    File No.: 811-23787

Dear Mr. Rosenberg:

The following responds to the comments you provided via email on April
25, 2022, in connection with your review of a registration statement (the “Registration Statement”) filed on Form N-2 under
the Investment Company Act of 1940, as amended (the “1940 Act”) to register Constitution Capital Private Markets Fund, LLC
(the “Company” or “Fund”), a registered closed-end fund. The changes to the Fund’s disclosure discussed
below are reflected in Pre-Effective Amendment No. 1 to the Fund’s Registration Statement (the “Revised Registration Statement”).

For your convenience, we have repeated each comment
below, and the Fund’s responses follow your comments. Capitalized terms not otherwise defined herein shall have the meaning ascribed
to them in the Registration Statement, unless otherwise indicated.

GENERAL COMMENTS

 1. Please tell us if you have presented any test the waters materials to potential investors in connection with this offering. If so,
we may have additional comments.

The Fund confirms that it has not provided test-the-waters materials to
potential investors in connection with this offering and does not intend to do so.

 2. We note that portions of the filing are incomplete. We may have additional comments on such portions when you complete them in a pre-effective
amendment, on disclosures made in response to this letter, on information supplied supplementally, or on exhibits added in any pre-effective
amendments.

The Fund acknowledges the Staff’s
comment and undertakes to address any further comments from the Staff.

 3. If you intend to omit certain information from the form of prospectus included with the registration statement that is declared effective
in reliance on Rule 430A under the Securities Act of 1933 (“Securities Act”) , please identify the omitted information to
us supplementally, preferably before filing the final pre-effective amendment.

The Fund will inform the Staff of omitted information
in reliance on Rule 430A under the Securities Act prior to seeking effectiveness of the Registration Statement.

 4. Please advise us whether you have submitted, or expect to submit, any exemptive applications or no-action requests in connection with
the registration statement.

The Fund intends to seek Multi-Class
Exemptive Relief and Co-Investment Exemptive Relief.  The Fund does not expect to submit any other exemptive application or
no-action request in connection with the Registration Statement.

 5. Please provide the name of the Company's independent registered public accounting firm in correspondence.

The Fund will identify its independent
registered public accounting firm in a future pre-effective amendment filing once approved by its board.

 6. Response to this letter should be in the form of a pre-effective amendment filed pursuant to Rule 472 under the Securities Act. Where
no change will be made in the filing in response to a comment, please indicate this fact in a supplemental letter and briefly state the
basis for your position.

The Fund intends to file a pre-effective
amendment pursuant to Rule 472 under the Securities Act incorporating the noted responses to the Staff’s comments.
The Fund also has filed this letter as correspondence with the SEC via EDGAR.

 7. Inasmuch as Section 8(c) of the Securities Act relates to post-effective amendments, please remove the check from the box next to
“when declared effective pursuant to Section 8(c)” on the facing sheet.

The requested change has been made
in the Revised Registration Statement.

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PROSPECTUS

Cover Page

 8. Here and throughout the prospectus, reference is made to the Fund investing in “high quality investments.” Please explain
how the Fund defines “high quality investments,” particularly in light of the Fund's speculative nature. For example, as described
in the “Investment Related Risk” section, the Fund has the “ability to invest in Portfolio Companies in the early phases
of development which can be highly risky due to the lack of a significant operating history, fully developed product lines, experienced
management, or a proven market for their products. The Fund Investments may also include Portfolio Companies that are in a state of distress
or which have a poor record, and which are undergoing restructuring or changes in management, and there can be no assurances that such
restructuring or changes will be successful.”

The following disclosure will be added to the Revised Registration
Statement:

The Fund defines “high quality investments”
as investments that reflect the Fund’s target underlying investment attributes, including but not limited to, (i) well-established
leaders / management teams, (ii) organizational depth, (iii) secular tailwinds, (iv) attractive financial profile with regard to growth,
profitability, capital intensity, solvency and liquidity, (v) structured with prudent levels of debt relative to comparable companies
in the industry, (iii) enterprise valuations at entry consistent with, or a discount to, public comparable companies and precedent transactions,
and (iv) clear and actionable value creation plans that minimize downside exposure. These target underlying investment attributes, in
addition to strategy- and security-specific considerations, inform how the Adviser approaches its assessment of investments in Private
Assets.

 9. Please revise the definition of “Private Assets” to include only private assets. Specifically, for each component of the
definition of “Private Assets”, insert “private”. For example revise (i) to state that it includes direct investments
in positions in private equity or debt of operating companies. Furthermore, please delete investments that are inherently not private,
e.g., money market funds and short-term treasuries.

The requested change has been made
in the Revised Registration Statement.

 10. Please disclose in the bullets on the cover page the expected amount of repurchases per quarter.

The requested change has been made
in the Revised Registration Statement.

Summary of terms and conditions
– The Fund (Page 1)

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 11. Please supplementally explain to the staff how the Predecessor Fund plans to transfer substantially all of assets into the Fund, consistent
with Section 17(a) of the Investment Company Act of 1940, as amended (the “1940 Act”). Additionally, please inform staff whether
the Fund will present the Predecessor Fund’s performance as its own, and if so, describe the basis for using the Predecessor Fund’s
performance as that of the Fund. We may have additional comments based on your response.

Pursuant to the GuideStone Financial, et al., SEC
No-Action Letter (pub. avail. December 27, 2006), Predecessor Fund will, at the time of the reorganization, transfer its portfolio securities
to the Fund in exchange for shares of the Fund. The Fund anticipates that as soon as possible after the effective date of its registration
statement and contemporaneously with the public offering of its shares, the Fund will acquire substantially all of the assets and liabilities
of the Predecessor Fund in exchange for shares of the Fund of equal U.S. dollar value, and the Predecessor Fund will simultaneously distribute
on a pro rata basis to the partners of the Predecessor Fund of all of the Fund shares received in exchange for their partnership interests
in the Predecessor Fund in liquidation of the Predecessor Fund. Further, the transactions contemplated by the Agreement are intended to
qualify as a nontaxable exchange under Section 351 of the Internal Revenue Code of 1986, as amended (the “Code”), followed
by a nontaxable distribution under Section 731 of the Code.

The Fund confirms that it will present the Predecessor
Fund’s performance as its own. The Fund believes the inclusion of the Predecessor Fund’s
performance is supported by the Growth Stock Outlook Trust letter (pub. avail. Apr. 15, 1986) and the Nicholas-Applegate Mutual
Funds letter (pub. avail. Aug. 6, 1996).

Summary of terms and conditions
– Investment objective and strategies (Page 1)

 12. Disclose in the Summary of Term and Conditions - Investment Objective and Strategies that: (i) the Fund may make investments outside
of the United States, including in emerging markets, (ii) the Fund’s investment strategies involve exposure to foreign currencies;
(iii) the Fund may seek to hedge all or a portion of the Fund’s foreign currency risk; and (iv) the Fund may hedge all or a portion
of its currency exposures.

The requested disclosure has been
added in the Revised Registration Statement.

 13. The third paragraph of this section provides that “Under normal market conditions, the Fund intends to invest and/or make capital
commitments of at least 80% of its net assets, plus any borrowing for investment purposes, in Private Assets.” Rule 35d-1 under
the 1940 Act provides that if a fund’s name suggests a type of investment, the fund must have a policy to invest “at least
80% of the value of its Assets in a particular type of investment . . . suggested by the Fund’s name[.]” Here the Fund’s
80% test would treat capital commitments the same as assets for purposes of the Fund’s 80% test. Please revise the Fund’s
80% policy to delete the reference to capital commitments, inasmuch as they would not be Fund assets invested in Private Assets.

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The Fund acknowledges receipt of the Staff’s comment.
The Fund believes capital commitments should be treated the same as Assets for purposes of the Fund’s 80% test since once the Fund
has made an investment into a private equity fund, the Fund does not have control of the timing of the capital being drawn, but it is
irrevocably committed. Moreover, the inclusion of capital commitments in the Fund’s 80% policy is consistent with the 80% policies
of other funds with similar names.

Summary of terms and conditions
–Purchasing Shares (Page 5)

 14. Please note that registered closed-end funds that invest more than 15% of their net assets in private funds have imposed a minimum
investment of at $25,000, with limited exceptions: (1) as to employees, officers or trustees of the fund, the adviser or their affiliates;
and (2) by the board based on its consideration of the investor’s overall relationship with the adviser or selling agent, including
consideration of the aggregate value of all accounts of clients of a selling agent investing in the fund for purposes of satisfying the
minimum investment amount. Please disclose that all current and future classes of shares will be subject to a $25,000 minimum initial
investment or explain to us why it would be appropriate for the Fund to offer shares without imposing this limitation.

The requested change has been made
in the Revised Registration Statement.

 15. Please disclose that shares will be sold to only to “qualified clients” within the meaning of Rule 205-3 under the Investment
Advisers Act of 1940, as amended, and “accredited investors” within the meaning of Rule 501 under the Securities Act. Please
state that the accredited investor and qualified client criteria will apply to all investors and will not be waived under any circumstances.

The Registration Statement currently
includes the following disclosure:

“Each prospective investor in the
Fund will be required to certify that it is a “qualified client” within the meaning of Rule 205-3 under the Advisers Act and
an “accredited investor” within the meaning of Rule 501 under the Securities Act of 1933, as amended (the “Securities
Act”). The criteria for qualifying as a “qualified client” and “accredited investor” are set forth in the
subscription documents that must be completed by each prospective investor.”

However, the Fund does confirm it will include additional
disclosure stating that the accredited investor and qualified client criteria will apply to all investors and will not be waived.

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Summary of terms and conditions
– Repurchases of Shares (Page 6)

 16. The fifth paragraph of this section states that the Fund reserves the right to reduce the amount to be repurchased from a shareholder
so that required capital balance will be maintained. Please provide the legal authority for this provision.

There is no formal legal authority for this provision.
However, it is common practice that has been allowed by the Staff with other registrants.

Summary of fund expenses
(Page 8)

 17. Disclosure in note 2 states that the Board is able to provide waivers for the Early Repurchase Fee based on a best interest determination.
Please revise such language and throughout the N-2 to ensure that any Early Repurchase Fee waiver will be applied uniformly to all shareholders.
Further, please confirm that to the extent the Fund determines to waive, impose scheduled variations of, or eliminate a repurchase fee,
it will do so consistently with the requirements of Rule 22d-1 under the 1940 Act as if the repurchase fee were a CDSL and as if the Fund
were an open-end investment company. Also, that the Fund’s waiver of, scheduled variation in, or elimination of, the repurchase
fee will apply uniformly to all shareholders of the Fund regardless of class.

The requested change has been made
in the Revised Registration Statement.

The also Fund confirms to the extent
the Fund determines to waive, impose scheduled variations of, or eliminate a repurchase fee, it will do so consistently with the requirements
of Rule 22d-1 under the 1940 Act as if the repurchase fee were a CDSL and as if the Fund were an open-end investment company. Also, the
Fund confirms that the Fund’s waiver of, scheduled variation in, or elimination of, the repurchase fee will apply uniformly to all
shareholders of the Fund regardless of class.

Use of Proceeds (Page 8)

 18. The first sentence of this section states that the proceeds from the sale of Shares will be invested “as soon as practicable
after receipt of such proceeds, consistent with market conditions and the availability of suitable investments.” This disclosure
is vague. Please disclose how long it is expected to fully invest the proceeds in accordance with the Fund’s investment objectives
and policies, the reasons for any anticipated lengthy delay in investing the proceeds, and the consequences of any delay. See Item 7.2
of Form N-2; see also Guide 1 to Form N-2 (providing that the reasons for the expected delay should be stated if the Fund expects the
investment period to exceed three months).

The requested change has been made
in the Revised Registration Statement.

Private equity market overview
– Private equity investment types (Page 12)

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 19. This section provides that the Fund may make Direct Investments alongside other investors in an operating company. Please respond
to the following:

 ● To the extent a Co-Investment is made through a vehicle, will the Fund include the expenses of the vehicle, including transactional
expenses, on the Acquired Fund Fees and Expenses line of the fee table?

The Fund so confirms.

 ● Please confirm that the Fund and any another entity advised by the Adviser or any other affiliate of the Fund will not invest in a
common portfolio company, unless such investments are consistent with existing staff no-action letters.

The Fund so confirms.

Investment process overview
– Portfolio planning (Page 14)

 20. As a non-diversified fund, the Fund should not state that it is seeking diversification, nor should it characterize itself as having
a diversification strategy.

The Fund has revised the disclosure to remove and replace
references to “diversification” and/or having a “diversification” str