AN ACR LTT HAD TO CLB IN RESPONSE TO A TCASII RA. THIS PUT IT IN CONFLICT WITH AN IFR ACFT ABOVE.

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APCHING THE SLI VOR; ATC CALLED TFC WE DID NOT SEE. THE FREQ WAS VERY BUSY WITH ALL TYPES OF TFC; AND WHILE APCHING THE SLI VOR WE RECEIVED A CALL FOR 9 O'CLOCK TFC; ALT UNKNOWN. SINCE MY FO WAS OFF THE FREQ GETTING THE ATIS AND MAKING A CALL TO THE COMPANY; I WAS LEFT FOR THE MOMENT TO FLY THE ACFT AND MAINTAIN A VISUAL SCAN FOR TFC WHEN THE TFC CALL WAS MADE BY ATC. IMMEDIATELY AFTER THE CALL; WE COMPLIED WITH A TCASII RA TO CLB. WHILE COMPLYING; I VISUALLY CONTACTED THE TFC AND AT THE SAME TIME; THE CLR OF CONFLICT MESSAGE WAS RPTED BY THE TCASII. OUR ALT WAS APPROX 4600 FT. ATC THEN MADE A CALL TO US THAT WAS PARTIALLY BLOCKED; AND THEN FOLLOWED BY A CALL TO A CHEROKEE IFR TFC AT 5000 FT; ADVISING THEM OF A TA ON OUR ACFT. AFTER CALLING ATC ON THE GND; THEY TOLD ME THEY WERE CONCERNED ABOUT MY ALTDEV; AND THE SUBSEQUENT LOSS OF VERT SEPARATION BTWN THE 2 IFR ACFT. I FEEL THERE WAS NO WAY TO AVOID THIS SIT. THE AREA WAS HEAVILY CONGESTED WITH A MIX OF IFR AND VFR ACFT. SO MUCH CONGESTION THAT APPROX 3 MINS LATER; WE WERE ISSUED ANOTHER TCASII RA ON ANOTHER ACFT. OUR OPS SPECS ARE QUITE CLR THAT WE MUST COMPLY WITH A TCASII RA. SINCE I WAS NOT MADE AWARE OF THE IFR TFC AT 5000 FT; I HAD NO WAY OF KNOWING THAT BY COMPLYING WITH THE TCASII RA; I WAS CLBING INTO ANOTHER ACFT.