ACR RECEIVES TCASII ON PREVIOUSLY ISSUED VFR TFC THAT WAS IN SIGHT AND CLBS TO AN OCCUPIED ALT RESULTING IN LTSS.

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I OBSERVED AN ACR MLG X AT 11000 FT SWBOUND CONVERGING WITH A VFR (UNIDENTED TARGET) NBOUND AT 10500 FT. ALSO CONVERGING NWBOUND WAS AN MLT Y DSNDING TO 12000 FT. I HEARD THE RADAR CTLR ISSUE A NEW ALT TO MLT Y TO STOP DSCNT AT 13000 FT. THE D AND R CTLRS BOTH ADVISED ME ACR X WAS MAKING A TCASII RA BY CLBING TO AVOID THE VFR. ACR X CLBED TO 12800 FT WHICH CAUSED A LOSS OF SEPARATION WITH MLT Y. TA'S WERE ISSUED. I FELT THE ACTIONS TAKEN BY THE RADAR CTLR WERE PROPER. I EXPECTED ACR X TO CLB 500 FT OR 1000 FT AT THE MOST TO PUT A BUFFER ON HIS TFC. THE PLT OF ACR X CLAIMED THE TCASII SHOWED 0 FT AND THE COPLT TOLD HIM THE TFC WAS 'CLBING INTO THEM.' I OBSERVED THE VFR'S MODE C SHOWING 105 (10500 FT) BEFORE; DURING; AND AFTER THE INCIDENT. SUPPLEMENTAL INFO FROM ACN 242304: THIS WAS A TCASII INDUCED SIT. ACR X WAS DSNDING FOR SJC TO 11000 FT. VFR TFC QUOTED XING L TO R AT 10500 FT. ACR X RPTED TFC 'AT HIS ALT AND CLBING' AND ACR X RESPONDED TO TCASII ALERT TO CLB. ZOA MODE C OF VFR SHOWED LEVEL AT 10500 FT AT ALL TIMES. ACR X PLT CLBED TO 12800 FT WHICH PUT HIM INTO CONFLICT WITH MLT Y AT 13000 FT. TFC QUOTED AND ACR X DSNDED AGAIN. IN MY OPINION A TCASII ALERT WAS UNNECESSARY. THE VFR SHOWED LEVEL AT 10500 FT AT ALL TIMES. I WAS QUOTING TFC AND ACR X WAS ASSIGNED 11000 FT. IN ADDITION I BELIEVE ACR X OVER-REACTED TO THE ALERT BY CLBING ALMOST 2000 FT. THIS PUT HIM IN JEOPARDY WITH MLT Y AT 13000 FT. SUPPLEMENTAL INFO FROM ACN 242084: I WAS WORKING D-RADAR SECTOR AT ZOA. THE RADAR SIDE CLRED AN ACR X TO 11000 FT. ACR X WAS LEVEL AT 11000 FT AND AN MLT WAS CLRED ABOVE ACR X TO 12000 FT. THE 2 ACFT WERE MERGING. THE RADAR CTLR ISSUED VFR TFC TO ACR X 12 O'CLOCK; 8 MI; 10500 FT. ACR X SAID 'THE TFC WAS AT HIS ALT AND THAT HE WAS CLBING.' LOSS OF SEPARATION OCCURRED AND ZOA INVESTIGATED THE INCIDENT.