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Faegre Drinker Biddle & Reath LLP

One Logan Square, Suite 2000

Philadelphia, Pennsylvania 19103

www.faegredrinker.com

August 19, 2022

Via EDGAR Transmission

Securities and Exchange Commission

100 F Street, N.E.

Washington, D.C. 20549

Attention: Michael A. Rosenberg and Ken Ellington

 Re: Constitution Capital Private Markets Fund, LLC

    File No.: 811-23787

Dear Messrs. Rosenberg and Ellington:

This letter supplements the letter dated June 28,
2022 and responds to the staff's disclosure and accounting comments provided via telephone on July 27, 2022 and July 29, 2022 in connection
with your review of the 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 “Fund”),
a registered closed-end fund. The changes to the Fund’s disclosure discussed below will be reflected in a pre-effective amendment
to the Fund’s 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.

DISCLOSURE COMMENTS

 1. We acknowledge your response to our prior comment 8. Please clarify that “high quality”
does not relate to the credit rating of the Fund’s investments but rather that within a risky investment universe the Fund seeks
what it deems to be high quality companies.

The Fund will revise the disclosure
as requested.

 2. We reiterate prior comment 13. The SEC staff position remains that capital commitments should not count
towards an 80% policy.

The above-referenced disclosure will be revised as follows
in the Revised Registration Statement:

“Under normal circumstances, the Fund intends to
invest (which for this purpose includes unfunded capital commitments) of at least 80% of its net assets (plus the amount of any borrowings
for investment purposes) in Private Assets.”

The registrant believes the revised disclosure is appropriate
and that unfunded 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 and investment strategies.

 3. With regards to your response to prior comment 16, this appears to be in contravention of Rule 13e-4(f)(8)(i)
that the tender offer must be open to all security holders of the class of securities subject to the tender offer. That means it must
be open to the same degree and in the same way, i.e. they must all get the same offer and be treated the same way. Also, in a partial
offer like these, the Fund is required by Rule 13e-4(f)(3) to accept tendered securities on a pro rata basis.

We have clarified the disclosure
to provide that the Fund will only reduce the amount to be repurchased to the extent consistent with the Exchange Act, including
the rules thereunder, and any other applicable laws.

 4. With regards to your response to prior comment 17, disclose under “Repurchases of Shares”
in the Prospectus and as a footnote to the fee table that to the extent the Fund determines to waive, impose scheduled variations of,
or eliminate an early repurchase fee, it will do so consistently with the requirements of Rule 22d-1 under the 1940 Act , and the Fund’s
waiver of, the scheduled variation in, or elimination of the early repurchase fee will apply uniformly to all shareholders regardless
of share class.

The Fund will revise the disclosure
as requested.

 5. With regards to your response to prior comment 20, balance the disclosure by disclosing that the Fund
is non-diversified under the 1940 Act.

The Fund will revise the disclosure
as requested.

 6. We understand that Delaware law permits a fund to eliminate or alter the fiduciary duties of trustees
or other persons and replace them with the standards set forth in the Limited Liability Company Agreement. Provisions eliminating or altering
the fiduciary duties of the Fund’s trustees, officers, etc. are inconsistent with federal securities laws and the Securities and
Exchange Commission’s express views on such persons’ fiduciary duties.

Please add a provision in the Fund’s LLC Agreement
or otherwise modify the LLC Agreement to clarify explicitly that notwithstanding anything to the contrary in the LLC Agreement, nothing
in the LLC Agreement modifying, restricting, or eliminating the duties or liabilities of members and former members of the Board and officers
and former officers of the Fund shall apply to or in any way limit the duties or liabilities of such persons with respect to matters arising
under the federal securities laws.

Registrant acknowledges the Staff’s comment,
but it believes the Fund’s LLC Agreement currently covers the abovementioned provision. Section 3.7(a) of the LLC Agreement states
the following:

The rights of indemnification provided under this Section 3.7
shall not be construed so as to provide for indemnification of an indemnitee for any Losses (including any liability under federal securities
laws which, under certain circumstances, impose liability even on persons that act in good faith) to the extent (but only to the extent)
that such indemnification would be in violation of applicable law, but shall be construed so as to effectuate the applicable provisions
of this Section 3.7 to the fullest extent permitted by law.

 7. Staff is unclear what the Fund’s approach to prior performance will be given that in your response to prior comment 11 it says
the Fund intends to adopt the Predecessor Fund’s performance as its own but then cites the Nicholas-Applegate Mutual Funds letter
(pub. avail. Aug. 6, 1996). Accordingly, please clarify if the Fund intends to adopt the Predecessor Fund’s performance as its own
in reliance on the MassMutual Institutional Funds letter (pub. avail. Sep. 28, 1995) or to include a performance composite in a section
entitled “Advisor Prior Performance Information” in the Prospectus in reliance on the Nicholas-Applegate No-Action Letter.
Regardless of the choice, please present the performance information consistent with the guidance in the appropriate No-Action Letter,
including all required disclosures.

The Fund no longer intends to provide prior performance
information in the Fund’s Registration Statement. The Fund will update the Registration Statement accordingly.

ACCOUNTING COMMENTS

 8. We acknowledge your response to our prior comment 33. The prior response does not appear to address applicable
U.S. Generally Accepted Accounting Principles where it is probable that the reporting entity will sell the underlying fund at an amount
different from net asset value through secondary market transactions. Please discuss how the entity will comply with ASC 820-10-35-62
related to sales on secondary markets.

The Registrant understands that the Fund is not permitted
to estimate the fair value of the underlying fund (or a portion of the investment) using the net asset value per share of the investment
(or its equivalent) as a practical expedient if, as of the reporting entity’s measurement date, it is probable that the reporting
entity will sell the investment for an amount different from the net asset value per share (or its equivalent). If the Registrant determines
that it is probable that it will sell an underlying fund for an amount different from the net asset value (or its equivalent), as described
in paragraph 820-10-35-62, the Fund will disclose the fair value of the investment or investments that meet this criteria and any remaining
actions that are required or needed to complete the sale.

 9. Please remove the disclosure from the Registration Statement stating that neither the Valuation Committee
nor the Adviser will generally have sufficient information in order to be able to confirm or review the accuracy of valuations provided
by Portfolio Fund Managers and include disclosure similar to your response to prior comment 34 stating that the Fund will consider whether
an adjustment to the most recent net asset value of its investments in Portfolio Funds is necessary based on available information to
estimate a net asset value that is calculated in a manner consistent with ASC Topic 820.

The Fund will revise the disclosure
as requested.

 10. We reiterate prior comment 31. Please include examples and a graphical representation demonstrating
the operation of the incentive fee in the prospectus.

The Registrant respectfully advises the Staff that it
continues to believe this type of disclosure to be inconsistent with current industry practice and regulatory requirements. Other closed-end
investment companies that have included a graphical representation of an incentive fee in their registration
statements differ materially in structure and operation from the Fund’s Incentive Fee because the incentive fees of those registrants
(i) are income only-related incentive fees (i.e., payable only on interest income, dividend income and any other income incurred during
the preceding calendar quarter) (“Income Only Incentive Fees”) and (ii) include the concept of a hurdle rate. Income Only
Incentive Fees may be paid by clients who are not “qualified clients” within the meaning of Rule 205-3 (“Rule 205-3”) under
the Investment Advisers Act of 1940, as amended (the “Advisers Act”).

However, in this case, the Fund’s
Incentive Fee is payable only on an increase in the Fund’s net asset value. Second, the Fund’s Incentive Fee does not include
the hurdle rate concept. Lastly, the Fund is offered only to investors that are both an “accredited investor” within the
meaning of Rule 501 of the Securities Act of 1933, as amended and a “qualified client” within the meaning
of Rule 205-3. The Commission adopted Rule 205-3 to provide a conditional exemption from the general prohibition on performance fees
for certain clients who are financially sophisticated or who have the resources to obtain sophisticated financial advice.1
In adopting Rule 205-3, the Commission reasoned that because of their wealth, financial knowledge and expertise, “qualified clients”
are less dependent on the protections that Section 205(a)(1) of the Advisers Act was intended to provide. In the 1985 Adopting Release,
the Commission indicated that clients who are able to understand and bear the risks of performance fees should have the opportunity to
participate in compensation arrangements that they and their advisers consider appropriate. Since all of the Fund’s investors will
be “qualified clients” that the Commission has determined by rule have the financial sophistication to understand the mechanics
of an incentive fee, the Registrant does not believe that it is necessary to include a graphical representation of an
incentive fee in the Fund’s registration statement for investor protection.

*             	*            	*

We trust that the foregoing is responsive to your comments. Questions
and comments concerning this filing may be directed to the undersigned at (215) 988-3307.

Sincerely,

/s/ Jillian L. Bosmann

Jillian L. Bosmann

 cc: Michael Spratt, Assistant Director

Michael Shaffer, Branch Chief

1
Exemption To Allow Registered Investment Advisers to Charge Fees Based Upon a Share of Capital Gains Upon or Capital Appreciation
of a Client’s Account, Investment Advisers Act Release No. 996 (Nov. 14, 1985)
(“1985 Adopting Release”).