FLC OVERSHOT A SID ALT DUE TO DISTR OF TCASII TA.

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THE NEWARK 4 DEP FOR RWY 4L IS NOT PARTICULARLY DIFFICULT; BUT IT MOVES QUICKLY AND REQUIRES A GOOD AMOUNT OF ATTN. AFTER LIFT OFF IT CALLS FOR A R TURN TO A 060 DEG HDG; THEN AT 4 DME A 130 DEG L TURN TO A 290 DEG HDG; WHILE LEVELING AT 2500 FT. DURING THIS THERE ARE OTHER NORMAL DUTIES INCLUDING WATCHING FOR TFC; SWITCHING TO DEP FREQ; AND SCHEDULED FLAP RETRACTION FROM A TKOF SETTING OF 15 DEG. AT 1500 FT MSL WITH THE CAPT FLYING; I CALLED '1000 FT TO GO.' WE WERE ALREADY AT 5 DEG FLAPS AND AS THE CAPT STARTED OUR L TURN THE TCASII RPTED AN AUDIBLE 'TA'. THE SCOPE SHOWED A TARGET IN FRONT OF AND BELOW US. IT MUST HAVE BEEN NEAR THE EDGE OF THE 'TA' SENSITIVITY AREA OF THE TCASII BECAUSE IT SOUNDED REPEATEDLY. ALTHOUGH IT NEVER ISSUED A 'RA' THIS CONSTANT DISTR DEMANDED OUR ATTN. WHILE TRYING TO MAKE VISUAL CONTACT AND RETRACTING FLAPS; THE CAPT AND I NOTICED AN ALT OF 2800 FT. BY THE TIME WE GOT INTO A DSCNT WE TOPPED OUT AT 2900 FT. WE QUICKLY RETURNED TO 2500. THE TCASII STOPPED ABOUT THE TIME WE NOTICED THE ALT. I THINK IT'S POSSIBLE THAT THE TCASII WARNINGS MAY HAVE URGED A CLB INSTINCTIVELY EVEN THOUGH IT NEVER ISSUED A 'RA.' THEN THE DISTRS HELPED US MISS OUR ALT. CORRECTIVE ACTIONS WOULD BE TO REDUCE OR DELAY SOME OF THE OVERLAPPING DUTIES DURING THIS EWR 4 DEP. FLAP RETRACTION SEEMS TO BE THE ONLY FLEXIBLE DUTY. ALTHOUGH DELAYING RETRACTION WILL GET YOU TO 2500 FT SOONER; THERE WILL BE ONE LESS DUTY FOR BOTH L AND R SEATS. TCASII WARNINGS HOWEVER DISTRACTING HAVE TO BE OBSERVED.