DURING CLB TO CRUISE ALT; A B757 CREW RECEIVE A TCASII RA THAT TURNED OUT TO BE 2 INTRUDER ACFT.

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THE FO WAS THE PF. WE WERE CLBING TOWARD FL230 WHEN WE CHKED IN WITH THE HIGH ALT SECTOR. THE CTLR CLRED US TO FL310. I ACKNOWLEDGED THE CLRNC; VERIFIED THE SETTING IN THE FLT DIRECTOR WINDOW AND THEN WE (FO AND I) REMARKED TO EACH OTHER ABOUT BEING CLRED TO OUR FLT PLAN ALT (FL310). AFTER PASSING FL280; WE GOT A TFC ALERT ON THE TCASII AND I SHOWED A YELLOW CIRCLE AT 12 O'CLOCK POS. BECAUSE THE TFC WAS AT THE EDGE OF THE DISPLAY; ONLY 1/2 OF THE SYMBOL WAS VISIBLE AND IT DID NOT SHOW ANY RELATED DATA; SO WE DID NOT KNOW IF THE TFC WAS ABOVE OR BELOW US. ABOUT THE SAME TIME WE HEARD ATC TELL ACR Z TO DSND BACK TO ALT.; THEN ATC ISSUED TFC TO US AT 12 O'CLOCK POS AT FL290. DURING THIS CALL; THE TCASII SWITCHED TO AN RA TELLING US TO DSND. WE BROKE THE CLB REACHING ABOUT FL288; THEN WE SAW AN RJ FLY OVER US IN THE OPPOSITE DIRECTION AT FL290. THINKING THAT THE RJ WAS OUR CONFLICT ACFT; WE EXPECTED THE RA TO CLR MOMENTARILY. ATC WAS TRYING TO GET ACR Z TO DSND; I BELIEVE; TO FL280. I WAS WORRIED THAT SOMEHOW ACR Z HAD STRAYED FROM THEIR ALT AND WERE CLBING TOWARD US. ACR Z RESPONDED THAT THEY WERE CLBING IN RESPONSE TO AN RA. WE THEN BEGAN TO REALIZE THAT OUR RA HAD NOT CLRED; SO WE WERE PROBABLY IN CONFLICT WITH ACR Z. THE RA WAS TELLING US TO DSND; SO WE BEGAN TO DO THAT; BUT THEN WE SAW ACR Z AHEAD AND ABOVE US; GOING THE OPPOSITE DIRECTION. IT LOOKED LIKE HE WAS SEVERAL HUNDRED FT ABOVE US. I RPTED THAT ACR Z WAS IN SIGHT AND WE WERE PASSING UNDER HIM OK. THEN OUR RA CLRED AND WE STARTED TO RESUME OUR CLB. AS WE STARTED TO CLB; ATC WAS STILL TRYING TO SORT OUT WHAT HAPPENED. THEN ATC DIRECTED US TO DSND TO FL280. WE STOPPED OUR CLB AT ABOUT FL292 AND THEN DSNDED TO FL280. AS WE WERE DSNDING TO FL289; I TOLD ATC THAT WE HAD GOTTEN AN RA AND HAD RESPONDED; HALTING OUR CLB. I ALSO REMINDED ATC THAT WE HAD BEEN CLRED TO FL310. AFTER LNDG; I CONTACTED ZAB AT THEIR REQUEST. I TALKED WITH THE SUPVR WHO INFORMED ME THAT IT WAS AN ATC ERROR. WE HAD BEEN CLRED TO FL310; SO IT WAS A CTLR ERROR. SUPPLEMENTAL INFO FROM ACN 624278: WHILE ENRTE TALKING TO ZAB; WE WERE CLRED TO CLB TO FL310. WHILE CLBING THROUGH APPROX FL280 WE RECEIVED TFC AND CLRNC QUESTIONS ON ANOTHER ACFT (LATER DETERMINED TO BE TFC #2 ACR MD80). SHORTLY THEREAFTER; WE RECEIVED AN RA TO DSND. WHILE RESPONDING TO THE RA; WE SAW AN RJ (TFC #1) FLY OVERHEAD. WE CONTINUED RESPONDING TO THE RA WHILE THE ATC CONGESTION AND CONFUSION CONTINUED; TRYING TO SORT OUT WHAT WAS GOING ON. AFTER CLRING THE CONFLICT; WE RECOMMENDED OUR CLB TO FL310. WE STEPPED ON EACH OTHER SEVERAL TIMES BEFORE FINALLY RECEIVING A CLRNC TO DSND IMMEDIATELY TO FL280. AFTER LNDG; WE CONTACTED ATC AND THEY ACCEPTED RESPONSIBILITY FOR THE ERROR. CONTRIBUTING FACTORS: SINCE ATC MISTAKES LIKE THIS RARELY HAPPEN; HAVING 2 CONFLICTING ACFT THAT CLOSE IN TRAIL REALLY ADDED TO THE CONFUSION. YOU USUALLY ASSOCIATE AN RA WITH 1 ACFT. WE HAVE BEEN FILING FOR FL310 ON THESE WBOUND RTES FOR SOME TIME; BUT NEVER RECEIVING IT. ON A PREVIOUS FLT; THE CAPT EVEN ASKED ATC WHY WE NEVER GET OUR REQUESTED ALT ANY MORE. ATC SAID THAT THERE IS SOME SORT OF ATC AGREEMENT THAT WE WILL NEVER GET FL310 ON THESE RTES. IF THAT IS THE CASE; THIS COULD BE PREVENTED IF WE STOP FILING FOR ALTS THAT WE SHOULD NOT RECEIVE DUE TO NEW ATC FLOW RESTRS.