A CL65 FLC HAS A POTENTIAL CONFLICT WITH ANOTHER ACR FLT WHEN ATC ASSIGNS THE SAME ALT FOR DSNDING CLBING TFC NEAR PHL; PA.

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CTR ISSUED A DSCNT TO FL190. I READ BACK THE CLRNC AND THE FO INITIATED DSCNT. AT ABOUT FL250; CTR REQUESTED THAT WE EXPEDITE TO FL190. I READ BACK THE CLRNC AND THE FO INCREASED DSCNT RATE TO 3000 FPM. THROUGH FL230; CTR REQUESTED THAT WE STOP DSCNT AT FL200. I READ BACK STOP AT FL200 AND THE FO RESET THE OTHER ACR ALT SELECT TO FL200. NEXT ATC XMISSION WAS TO ACFT Y; TELLING THEM TO STOP CLB AT FL200 DUE TO TFC. THE FO AND I BOTH HEARD THIS AND AGREED WE DIDN'T LIKE THE SIT. I QUERIED ATC ABOUT OUR ALT; ASKING HIM TO CONFIRM FL200. ATC REPLIED; 'NO; YOU SHOULD BE STOPPING AT FL210.' WE WERE LEVELING AT FL200 AT THIS TIME; SO I RPTED TO ATC THAT WE WERE AT FL200. HE SAID OK; AND GAVE OTHER ACR ACFT Y A TURN. AT THIS TIME WE GOT AN RA COMMANDING 'MONITOR VERT SPD.' ATC SAID 'ACFT X DSND NOW TO FL190;' WHICH I READ BACK. FO BEGAN A DSCNT. AT THIS TIME; ACFT Y RPTED THAT THEY WERE CLBING; I ASSUME THIS WAS DUE TO AN RA. I BELIEVE THAT THIS SIT WAS CREATED BY A MISCOM FROM ATC; CONTRIBUTING WAS A LACK OF SITUATIONAL AWARENESS BY ACFT Y IN ACCEPTING FL200.