ARTCC ARTCC INTRAFAC COORD ACR X ASSIGNED WRONG ALT. ACR X NON ADHERENCE TO ATC INSTRUCTIONS HAD LTSS FROM ACR Y. SYS ERROR. PLTDEV.

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ACR X DEPARTS BUF CLBING TO FL330 GOING TO BDL. ENRTE; THE PLT REQUESTS FL370 WITH ZOB. ZOB CALLS MY SECTOR (RKA) AND MAKES THE REQUEST WITH MY RADAR ASSOCIATE; WHICH HE DENIES DUE TO A HVY WBOUND FLOW AT FL350. ZOB IS TOLD TO STOP X AT FL330. AT THIS TIME; I WAS INVOLVED WITH ANOTHER CONFLICT OF 2 ACFT AT FL350 ON CONVERGING COURSES DUE TO WX DEVS. THESE 2 ACFT REQUIRED IMMEDIATE ATTN. DURING THE TIME OF THIS CONFLICT; X CHKED ON FREQ OUT OF FL322 FOR FL370. I DID NOT COPY THE INCORRECT ALT AS I WAS DISTR BY THE PREVIOUS SIT. UPON NOTICING X CLBING THROUGH FL340; I QUESTIONED THE PLT AND HE STATED HE HAD A CLRNC TO FL370. I IMMEDIATELY TURNED X TO A 080 DEG HDG AND ISSUED A DSCNT CLRNC. I RECEIVED A READBACK; QUICKLY FOLLOWED BY ANOTHER VOICE QUESTIONING WHY HE HAD TO DSND TO FL280. I BEGAN TO TRY TO EXPLAIN BUT REALIZED I HAD NO TIME AND TOLD X 'DSND NOW TO FL280 FLY HDG 080 DEGS. ANY FURTHER L TURN WOULD HAVE PUT X IN CONFLICT WITH OTHER ACFT. IN MY OPINION; HAD THE PLT COMPLIED WITH MY CLRNC WHEN IT WAS INITIALLY ISSUED; THE 080 DEG HDG WOULD HAVE PROVIDED SEPARATION. X CONTINUED TO CLB AND SHOWED NO INDICATION OF TURNING. I TURNED X FURTHER TO A HDG OF 060 DEGS AND TOLD HIM TO EXPEDITE HIS DSCNT. AGAIN THE PLT QUESTIONED THE CLRNC. ACR Y (THE WBOUND ACFT) WAS TURNED TO A 260 DEG HDG AND AT THAT POINT SEPARATION WAS LOST. X WAS THEN IN CONFLICT WITH SEVERAL OTHER WBOUND ACFT WHICH REQUIRED DRASTIC VECTORS TO MAINTAIN SEPARATION. X WAS AGAIN TOLD TO EXPEDITE DSCNT. AGAIN NO READBACK; THE RESPONSE: 'WHAT IS GOING ON?'