ACR X (SAME COMPANY SIMILAR CALL SIGN AS ACR Z) READ BACK ACR Z CLRNC. UNAUTHORIZED CLB THROUGH OCCUPIED ALT HAD LTSS FROM CPR Y. SYS ERROR.

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THE RADAR SECTOR WAS VERY BUSY WITH NUMEROUS DEPS CLBING E OFF OF DETROIT AND ARRS TO CLEVELAND FROM THE NW. ALSO TSTMS WERE IMPACTING THE SURROUNDING AIRSPACE WITH SEVERAL ACFT DEVIATING. A CLEVELAND INBOUND; CPR Y WAS DSNDING TO 160 ALONG V103. ACR X DEPARTED DTW AND CHKED IN CLBING TO 103. HE WAS RECLRED TO 150 AND TURNED TO FACILITATE LATERAL SEPARATION FROM CPR Y. HE ACKNOWLEDGED. ACR Z WAS CLRED TO FL240 SEVERAL MOMENTS LATER. ACR X TOOK THIS CLRNC AND CLBED THROUGH 150 RESULTING IN LOST SEPARATION WITH CPR Y. WHEN THIS WAS OBSERVED; ACR X WAS RECLRED TO 150 AND BOTH ACFT WERE ISSUED TURNS. SEPARATION WAS REESTABLISHED AND BOTH ACFT PROCEEDED ON COURSE. THE PRIMARY FACTOR WAS A MISSED READBACK AND A WRONG CLRNC TAKEN. CONTRIBUTING TO THIS WAS THE WX; WORKLOAD AND SIMILAR CALL SIGNS. SUPPLEMENTAL INFO FROM ACN 215060: ACR X LEVEL AT 15000 FT. SEVERAL ACFT; INCLUDING US; DEVIATING AROUND TSTMS. THERE WAS A LOT OF CONFUSION; MANY SPECIAL REQUESTS; AND SEVERAL ACFT WITH SIMILAR CALL SIGNS. THE FO ACKNOWLEDGED A CLRNC TO FL240. JUST PRIOR TO 16000 FT THE ATC CTLR TOLD US TO GO BACK TO 15000 FT. IT WAS NOT CLR IF WE HAD ACCEPTED ANOTHER ACFT'S CLRNC TO 24000 OR IF THE CTLR HAD GIVEN IT TO US BY MISTAKE. A COUPLE MINS LATER THE SAME CTLR GAVE US A CLRNC TO FL230. AGAIN AFTER WE WERE ABOUT TO PASS 16000 FT HE CANCELLED THE CLRNC AND TOLD US TO MAINTAIN 16000 FT. WE LOOKED FOR (BOTH VISUALLY AND WITH TCASII) ANY CONFLICTING TFC AND SAW NONE.