AN ALTDEV ON CLBOUT CAUSED LTSS.

Narrative

CLBING OUT ON THE WORTH 5 DEP PASSING APPROX 9000 FT MSL; WE RECEIVED A 'REDUCE CLB' RA. WE HAD NUMEROUS TARGETS SHOWING WITHIN THE 10 MI RANGE WITH A RED TARGET WITHIN 3 MI AT OUR 11 O'CLOCK POS TRAVELING IN THE OPPOSITE DIRECTION. THE CAPT WAS FLYING AND WE BOTH WERE LOOKING OUT TO MAKE SURE WE HAD THE SUSPECT ACFT IN SIGHT. I GLANCED IN AND NOTICED ANOTHER RED TARGET WITHIN APPROX 3 MI AT OUR 1 O'CLOCK; SAME ALT; COMING AT US. I LOOKED OUT AND SPOTTED THE PLANE HEADING STRAIGHT OVER US AT APPROX 2-3 MI. JUST ABOUT THAT TIME; WE RECEIVED AN ALT ALERT PASSING APPROX 10250 FT MSL. THE CAPT CORRECTED TO LEVEL FLT; REACHING APPROX 10400 FT MSL MOMENTARILY. CTR THEN ASKED US IF WE WERE STOPPING OUR CLB AT 10000 FT BECAUSE WE HAD TFC AT 11 O'CLOCK. ALSO; JUST BEFORE ALL THIS OCCURRED; WE HAD BEEN GIVEN SEVERAL OTHER TFC CALLOUTS; SO WE WERE BUSY LOOKING OUT. ALTHOUGH WE DID BUST THE ALT; I FEEL THE ATTN DIVERTED OUTSIDE WAS NECESSARY BECAUSE OF THE CLOSENESS OF THESE 2 AIRPLANES. I HAVE NEVER BEEN SO CLOSE TO MULTIPLE AIRPLANES ON DEP BEFORE. I GUESS ONE MIGHT SAY THE SOLUTION WOULD BE TO PAY BETTER ATTN; BUT I REALLY DON'T FEEL WE WERE NEGLIGENT BASED ON THE SIT. WE WERE PAYING ATTN; BUT THERE SEEMED TO BE PLANES TOO CLOSE SO OUR ATTNS NEEDED TO BE DIVERTED OUTSIDE AT THAT MOMENT. CONDITIONS WERE DAY AND CLR.