SecProbe.io

CORRESP
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Faegre Drinker Biddle & Reath LLP

One Logan Square, Suite 2000

Philadelphia, Pennsylvania 19103

www.faegredrinker.com

September 22, 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 responds to the staff's disclosure
and accounting comments provided via telephone in connection with your review of pre-effective amendment no. 1 to 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.

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. The prospectus provides that “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.”
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.

Upon consideration of the Staff’s comment and subsequent
discussions with the Staff, the Fund will change its name to “Constitution Capital Access Fund, LLC” in its definitive
registration statement filed pursuant to Rule 424 to comply with the Staff’s position that under Rule 35d-1, unfunded capital commitments
should not be included in the 80% policy of a fund with “Private Markets” in its name.

ACCOUNTING COMMENTS

 2. Please include examples demonstrating the operation of the incentive fee in the prospectus.

The following disclosure will be added to the Fund’s
Registration Statement:

Incentive Fee Examples.

Example 1 illustrates the calculation of the Fund's net
profits with respect to a Class of Shares and resulting Incentive Fee for a fiscal year. For illustrative purposes, assume (a) no Shares
of such Class are tendered for repurchase throughout the hypothetical fiscal year; (b) no new Shares of such Class are issued during such
fiscal year other than in connection with the reinvestment of dividends; (c) all dividends paid in respect of such Class during such fiscal
year are reinvested in additional Shares of such Class; and (d) the balance in the Loss Recovery Account maintained for such Class at
the beginning of the fiscal year equals $0.

    Example 1

    $100,000,000

    Net asset value of the applicable Class on April 1st

    $10,000,000

    Realized or unrealized increase in the fair market value
    of the Fund's investments attributable to such Class from April 1st to March 31st

    $(1,575,000)

    Aggregate Investment Management Fees accrued during fiscal
    year in respect of such Class

    $(750,000)

    Aggregate operating expenses accrued during fiscal year
    in respect of such Class

    $107,675,000

    Net asset value of the applicable Class on March 31st
    prior to accrual of Incentive Fee (i.e., April 1st net asset value increased by investment profits and decreased by Investment Management
    Fees and operating expenses borne by the Fund and attributable to such Class)

    $7,675,000

    Net profits for fiscal year (i.e., the excess of March
    31st net asset value of $107,675,000 over April 1st net asset value of $100,000,000)

    $767,500

    Incentive Fee payable to the Adviser in respect of such Class

    2

Example 2 illustrates the increase in the balance of
the Fund's Loss Recovery Account with respect to a Class of Shares at the end of a fiscal year in which the Fund experienced net losses.
For illustrative purposes, assume (a) no Shares of such Class are tendered for repurchase throughout the hypothetical fiscal year; (b)
no new Shares of such Class are issued during such fiscal year other than in connection with the reinvestment of dividends; (c) all dividends
paid in respect of such Class during such fiscal year are reinvested in additional Shares of such Class; and (d) the balance in the Loss
Recovery Account maintained with respect to such Class at the beginning of the fiscal year equals $0.

    Example 2

    $100,000,000

    Net asset value of the applicable Class on April 1st

    $(7,800,000)

    Realized or unrealized decrease in the fair market value
    of the Fund's investments attributable to such Class from April 1st to March 31st

    $(1,441,500)

    Aggregate Investment Management Fees accrued during fiscal
    year in respect of such Class

    $(758,500)

    Aggregate operating expenses accrued during fiscal year in respect of such Class

    $90,000,000

    Net asset value of the applicable Class on March 31st
    (i.e., April 1st net asset value decreased by investment losses and further decreased by Investment Management Fees and operating expenses
    borne by the Fund and attributable to such Class)

    $(10,000,000)

    Net losses for fiscal year (i.e., the excess of April
    1st net asset value of $100,000,000 over March 31st net asset value of $90,000,000)

    $10,000,000

    Loss Recovery Account balance as of March 31st, reflecting
    the addition of the Fund's net losses attributable to such Class for the fiscal year

    $0

    Incentive Fee payable to the Adviser in respect of such
    Class

    3

Example 3 illustrates the adjustment to the Fund's Loss
Recovery Account with respect to a Class of Shares at the end of a fiscal year in which the Fund has realized net profits. For illustrative
purposes, assume (a) no Shares of such Class are tendered for repurchase throughout the hypothetical fiscal year; (b) no new Shares of
such Class are issued during such fiscal year other than in connection with the reinvestment of dividends; (c) all dividends paid in respect
of such Class during such fiscal year are reinvested in additional Shares of such Class; and (d) the balance in the Loss Recovery Account
maintained with respect to such Class at the beginning of the fiscal year equals $10,000,000.

    Example 3

    $90,000,000

    Net asset value of the applicable Class on April 1st

    $10,000,000

    Balance of the Loss Recovery Account with respect to
    such Class on April 1st

    $11,150,000

    Realized or unrealized increase in the fair market value
    of the Fund's investments attributable to such Class from April 1st to March 31st

    $(1,443,625)

    Aggregate Investment Management Fees accrued during fiscal
    year in respect of such Class

    $(716,375)

    Aggregate operating expenses accrued during fiscal year in respect of such Class

    $99,000,000

    Net asset value of the applicable Class on March 31st
    (i.e., April 1st net asset value increased by investment profits and decreased by Investment Management Fees and operating expenses borne
    by the Fund and attributable to such Class)

    $9,000,000

    Net profits for fiscal year (i.e., the excess of March
    31st net asset value of $99,000,000 over April 1st net asset value of $90,000,000)

    $1,000,000

    Loss Recovery Account balance as of March 31st (i.e.,
    reflecting the subtraction of net profits of $9,000,000 from the April 1st balance of $10,000,000)

    $0

    Incentive Fee payable to the Adviser in respect of such
    Class (no Incentive Fee is payable because the balance in the Loss Recovery Account is still positive)

    4

Example 4 illustrates the effect of quarterly repurchases
of the Fund's shares on the calculation of the Quarterly Payments. For illustrative purposes, assume (a) the Fund has a balance in the
Loss Recovery Account with respect to a Class of Shares at the beginning of the relevant quarter of $1 million; (b) 5% of the Shares of
such Class are repurchased in a repurchase offer (meaning that 5% of the Fund's assets attributable to such Class are paid out to tendering
shareholders); and (c) the Fund has net profits attributable to such Class for such Fiscal Period (which is not the end of the Fund's
fiscal year) of $10 million, then (a) as illustrated above, the balance in the Loss Recovery Account maintained with respect to such Class
will be reduced from $1 million to zero; and (b) the Adviser will receive a Quarterly Payment of $45,000, based on the following:

    Example 4

    $10 million

    ($1 million)

    Net profits for the Fiscal Period attributable to such
    Class

    Amount required to eliminate the balance in the Loss
    Recovery Account with respect to such Class

    $9 million

    x 10%

    Net profits for the Fiscal Period after the balance of
    the Loss Recovery Account is eliminated

    Amount of Incentive Fee rate

    $900,000

    x 5%

    Incentive Fee

    Proportion of the Fund's assets attributable to such
    Class paid out to tendering shareholders

    $45,000

    Amount of Quarterly Payment paid to the Adviser

    5

Example 5 illustrates the
impact of maintaining a single Loss Recovery Account for each Class of Shares as a whole rather than separate loss recovery accounts
for each individual shareholder of such Class. For illustrative purposes, assume (a) no Shares are tendered for repurchase throughout
the hypothetical fiscal year; (b) no new Shares of such Class are issued during such fiscal year other than in connection with the reinvestment
of dividends; (c) all dividends paid in respect of such Class during such fiscal year are reinvested in additional Shares of such Class;
and (d) the balance in the Loss Recovery Account maintained with respect to such Class at the beginning of such fiscal year equals $0.

    Example
    5

    $100 million

    Net asset value of the
    applicable Class on April 1st ($10 per Share)

    $120 million

    Net asset value of the
    applicable Class on January 31st ($12 per Share). On February 1st, Shareholder X acquires Shares of such Class at $12 per Share.

    $110 million

    Net asset value of the
    applicable Class on March 31st prior to calculation of the Incentive Fee ($11 per Share)

    $10 million

    Net profits for the fiscal
    year ended March 31st attributable to such Class

    x 10%

    Amount of Incentive Fee
    rate

    $1 million

    Incentive
    Fee payable to the Adviser in respect of such Class ($0.10 per Share).

    $109 million

    Net asset value of the
    applicable Class on March 31st after deduction of the Incentive Fee ($10.90 per Share). Shareholder X bears a $0.10 per Share Incentive
    Fee notwithstanding that the Shares for which Shareholder X subscribed on February 1st have lost value since the date of Shareholder
    X's initial investment.

For purposes of determining the Fund's
net asset value attributable to any Class of Shares, the Incentive Fee will be calculated and accrued as an expense of the Fund attributable
to such Class (as if the last day of each month is the end of the Fund's fiscal year).

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 3. Please update the Predecessor Fund financial statements to include the disclosure required when net
asset value is used as a practical expedient. For example, include the strategy of the underlying fund, a description of the redemption
terms, etc. See ASC 820-10-50-6A.

The Registrant acknowledges the Staff’s
comment and notes the following:

 · For those investments using NAV as a practical expedient, the Predecessor Fund has indicated within the footnote of its Schedule
of Investments (page A-4 of the Registration statement), that the “Investment does not allow redemption or withdrawals except at
discretion of its general partner, manager, or advisor”, which incorporates the description of redemption terms in accordance with
ASC 820-10-50-6A.

 · The Fund includes enhanced disclosures in the prospectus of the Registration Statement that summarizes the terms of the investments
and its investment strategies of the underlying funds in accordance with ASC 820-10-50-6A. (pages 14, 32-33)

The Predecessor Fund will not be updating its financial
statements included in the Registration Statement. However, the Fund will make the requested changes in its future shareholder reports.

*           *           *

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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

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