MD80 CREW IS ISSUED A TCASII TA; RA; AND AN ENHANCED RA. WARNINGS ARE TO AVOID TWO OTHER ACFT.

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I WAS THE CAPT FLYING FROM LGB TO DFW. THE IFR DEP CLRNC WAS AT 1500 FT TURN L TO 180 DEGS AND MAINTAIN 3000 FT. ON A HDG OF 180 DEGS AND 3000 FT APPROX 5 NM SW OF LGB TCASII GAVE A TA ON TFC AT 1 O'CLOCK POS AND 7 NM FOLLOWED SHORTLY BY AN RA OF 1000-1500 FPM CLB. A CLB WAS BEGUN AND THE TFC WAS SIGHTED BY THE CAPT FO. APPROX 10 SECONDS LATER A 'MONITOR VERT SPD' COMMAND WAS GIVEN BY TCASII. I LOOKED AT THE TCASII DISPLAY WHICH INDICATED THE CONFLICTING TARGET AT 11 O'CLOCK POS LESS THAN 1 MI. I SIGHTED THE TFC AT 11 O'CLOCK POS AND MAINTAINED APPROX 1000 FPM CLB (GREEN BAND) AND MISSED THE LIGHT TWIN AT 11 O'CLOCK POS BY LESS THAN 200 FT VERT AND 200 FT HORIZ. WE CLBED TO APPROX 3400-3500 FT AS COMMANDED BY THE TCASII RA. DEP CTL WAS NOTIFIED OF OUR RA AND CLB. SUMMARY: THE FO STATED 'I THINK WE WOULD HAVE HIT THE 1 O'CLOCK POS TFC IF WE HAD NOT CLBED.' I THEREFORE THINK THE TCASII RA OF THE 1 O'CLOCK POS TARGET WAS CORRECT BUT THE RESULTING CLB PUT US IN VERY CLOSE PROX TO THE 11 O'CLOCK POS TARGET. DEP CTL WAS OF NO HELP; NO ADVISORIES; NO TURNS; NO HELP. I CAN'T BELIEVE THAT IN A HIGH DENSITY AREA SUCH AS LAX-LGB THAT 500 FT SEPARATION EXIST BTWN IFR AND VFR TFC.