Sec Form 4 Filing - DAVIDSON KEMPNER CAPITAL MANAGEMENT LP @ BMC STOCK HOLDINGS, INC. - 2016-05-18

FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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1. Name and Address of Reporting Person DAVIDSON KEMPNER CAPITAL MANAGEMENT LP 2. Issuer Name and Ticker or Trading Symbol BMC STOCK HOLDINGS, INC. [ STCK] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director X __ 10% Owner _____ Officer (give title below) _____ Other (specify below) (Last) (First) (Middle) 520 MADISON AVENUE, 30TH FLOOR 3. Date of Earliest Transaction (MM/DD/YY) 05/18/2016 (Street) NEW YORK, NY10022 4. If Amendment, Date Original Filed (MM/DD/YY) 6. Individual or Joint/Group Filing (Check Applicable Line) _____ Form filed by One Reporting Person __ X __ Form filed by More than One Reporting Person (City) (State) (Zip)

Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned 1.Title of Security (Instr. 3) 2. Transaction Date (MM/DD/YY) 2A. Deemed Execution Date, if any (MM/DD/YY) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Stock, par value $0.01 ("Common Stock") 05/18/2016 G 10,667 D $ 0 10,903,316 ( 1 ) I See footnotes ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 ) Common Stock 05/18/2016 S 1,589,333 D $ 17 9,313,983 I See footnotes ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) ( 7 )

Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned ( e.g. , puts, calls, warrants, options, convertible securities) 1. Title of Derivative Security (Instr. 3) 2. Conversion or Exercise Price of Derivative Security 3. Transaction Date (MM/DD/YY) 3A. Deemed Execution Date, if any (MM/DD/YY) 4. Transaction Code (Instr. 8) 5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5) 6. Date Exercisable and Expiration Date (MM/DD/YY) 7. Title and Amount of Underlying Securities (Instr. 3 and 4) 8. Price of Derivative Security (Instr. 5) 9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4) 10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4) 11. Nature of Indirect Beneficial Ownership (Instr. 4) Code V (A) (D) Date Exercisable Expiration Date Title Amount or Number of Shares

Reporting Owners Reporting Owner Name / Address Relationships Director 10% Owner Officer Other DAVIDSON KEMPNER CAPITAL MANAGEMENT LP 520 MADISON AVENUE 30TH FLOOR NEW YORK, NY10022 X KEMPNER THOMAS L JR DAVIDSON KEMPNER CAPITAL MANAGEMENT LP 520 MADISON AVENUE, 30TH FLOOR NEW YORK, NY10022 X YOSELOFF ANTHONY ALEXANDER DAVIDSON KEMPNER CAPITAL MANAGEMENT LP 520 MADISON AVENUE, 30TH FLOOR NEW YORK, NY10022 X BASTABLE CONOR DAVIDSON KEMPNER CAPITAL MANAGEMENT LP 520 MADISON AVENUE, 30TH FLOOR NEW YORK, NY10022 X FRIEDMAN AVRAM Z DAVIDSON KEMPNER CAPITAL MANAGEMENT LP 520 MADISON AVENUE, 30TH FLOOR NEW YORK, NY10022 X Signatures /s/ Avram Z. Friedman 05/20/2016 Signature of Reporting Person Date /s/ Davidson Kempner Capital Management LP, By: Thomas L. Kempner, Jr., its Executive Managing Member 05/20/2016 Signature of Reporting Person Date /s/ Thomas L. Kempner, Jr. 05/20/2016 Signature of Reporting Person Date /s/ Anthony A. Yoseloff 05/20/2016 Signature of Reporting Person Date /s/ Conor Bastable 05/20/2016 Signature of Reporting Person Date

Explanation of Responses:

( 1 )The Form 3 filed by the Reporting Persons on December 11, 2015 reported 10,913,993 shares of Common Stock instead of 10,913,983 shares. The Form 3 overstated the number of shares by 10 shares due to a rounding error. ( 2 )The securities to which this filing relates are held directly by (i) M. H. Davidson & Co., a New York limited partnership ("CO"), (ii) Davidson Kempner Partners, a New York limited partnership ("DKP"), (iii) Davidson Kempner Institutional Partners, L.P., a Delaware limited partnership ("DKIP"), (iv) Davidson Kempner International, Ltd., a British Virgin Islands business company ("DKIL"), (v) Davidson Kempner Distressed Opportunities Fund LP, a Delaware limited partnership ("DKDOF"), (vi) Davidson Kempner Distressed Opportunities International Ltd., a Cayman Islands exempted company ("DKDOI"), (vii) Davidson Kempner Long-Term Distressed Opportunities Fund LP, a Delaware limited partnership ("DKLTDO"), (continued in footnote (3)) ( 3 )(continued from footnote (2)) (viii) Davidson Kempner Long-Term Distressed Opportunities International Master Fund LP, a Cayman Islands exempted limited partnership ("DKLTDI"), (ix) Davidson Kempner Long-Term Distressed Opportunities Fund II LP, a Delaware limited partnership ("DKLTDO II") and (x) Davidson Kempner Long-Term Distressed Opportunities International Master Fund II LP, a Cayman Islands exempted limited partnership ("DKLTDI II"). ( 4 )M.H. Davidson & Co. GP, L.L.C., a Delaware limited liability company, is the general partner of CO. MHD Management Co., a New York limited partnership ("MHD"), is the general partner of DKP and MHD Management Co. GP, L.L.C., a Delaware limited liability company is the general partner of MHD. Davidson Kempner Advisers Inc., a New York corporation, is the general partner of DKIP. DK Group LLC, a Delaware limited liability company, is the general partner of DKDOF. DK Management Partners LP, a Delaware limited partnership, is the investment manager of DKDOI. Davidson Kempner Long-Term Distressed Opportunities GP LLC, a Delaware limited liability company, is the general partner of DKLTDO and DKLTDI. Davidson Kempner Long-Term Distressed Opportunities GP II LLC, a Delaware limited liability company, is the general partner of DKLTDO II and DKLTDI II. ( 5 )Davidson Kempner Capital Management LP, a Delaware limited partnership ("DKCM") and a registered investment adviser with the U.S. Securities and Exchange Commission, acts as investment manager to each of CO, DKP, DKIP, DKIL, DKDOF, DKDOI, DKLTDO, DKLTDI, DKLTDO II and DKLTDI II either directly or by virtue of a subadvisory agreement with the investment manager of the relevant fund. DKCM GP LLC, a Delaware limited liability company, is the general partner of DKCM. ( 6 )The managing members of DKCM are Messrs. Thomas L. Kempner, Jr., Timothy I. Levart, Robert J. Brivio, Jr., Eric P. Epstein, Anthony A. Yoseloff, Avram Z. Friedman, Conor Bastable, Morgan P. Blackwell, Shulamit Leviant, Patrick W. Dennis and Gabriel T. Schwartz. Messrs. Thomas L. Kempner, Jr., Anthony A. Yoseloff, Conor Bastable and Avram Z. Friedman through DKCM, are responsible for the voting and investment decisions relating to the securities held by CO, DKP, DKIP, DKIL, DKDOF, DKDOI, DKLTDO, DKLTDI, DKLTDO II and DKLTDI II reported herein. ( 7 )The filing of this statement shall not be deemed an admission that any of the Reporting Persons is the beneficial owner of the securities reported herein for purposes of Section 16 of the Securities Act of 1934, as amended, or otherwise. Each of the Reporting Persons expressly disclaims beneficial ownership of the securities reported herein except to the extent of its or his pecuniary interest therein.

Remarks: To enable all of the Reporting Persons to gain access to the Securities and Exchange Commission's electronic filing system (which only accepts a maximum of 10 joint filers per report), this report is the second of two identical reports relating to the same transaction being filed with the Securities and Exchange Commission.

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.

* If the form is filed by more than one reporting person, see Instruction 4(b)(v).

** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).

Note: File three copies of this Form, one of which must be manually signed. If space is insufficient, see Instruction 6 for procedure.
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