ACR X DSCNT THROUGH OCCUPIED ALT RECEIVED TCASII RA DSND HAD LTSS FROM ACR Y. SYS ERROR.

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ACR X PROCEEDED NBOUND ON J121 TOWARD SIE; 114.8; FL290; 250 KTS. OUR RADAR SHOWED SOME WX IN THE VICINITY OF SIE. WE COULD ALSO VISUALLY SEE THE WX. WE REQUESTED DEV TO THE W TO GET AROUND THE UPWIND SIDE; BUT WAS TOLD BY ATC WE COULD DEVIATE E; SO WE DID. AS WE WERE APPROX ABEAM SIE TO THE E; APPROX HDG 050 DEGS; ATC ASKED IF WE COULD COME TO A 300 DEG HDG. I REPLIED 'I'D RATHER CONTINUE STRAIGHT AHEAD.' WE WERE IN THE CLR; BELOW THE OVERHANG AND SMOOTH. ATC RESPONDED 'CONTINUE STRAIGHT AHEAD.' SHORTLY AFTER THIS WE WERE GIVEN A DSCNT TO FL240; AMENDED TO FL270. WE BEGAN A DSCNT TO FL270. AS WE WENT THROUGH FL280; WE GOT A TCASII RA THAT COMMANDED A GREEN AREA DSCNT; 2000 FPM ON VSI. WE WERE DSNDING AT 1500 FPM AT THE TIME. WE RESPONDED TO THE COMMAND AND LEVELED AT FL270. CTR SEEMED TO BE EXCITED AT THIS TIME AND RESPONDED 'ACR X I SEE YOU'RE LEVEL FL270' TO WHICH WE RESPONDED; YES FL270. AS I LOOKED TO MY L TO SEE THE TFC; I COULD SEE ACR Y IN THE DISTANCE; IN A HOLDING PATTERN TURN IN THE VICINITY OF BOTON INTXN; N OF SIE. ACR Y RESPONDED THAT HE HAD A TCASII ADVISORY ALSO; APPROX 3 MI. CTR ASKED IF WE HAD BEEN GIVEN A HOLD AT SIE; TO WHICH WE RESPONDED NO. WE WERE THEN VECTORED; BASICALLY IN A R 360 DEG TURN; AND DSNDED ON THE GAMRN ARR TO JFK.