ATX LTT ALT DEVIATION OVERSHOT DURING CLIMBOUT FROM VNY RESULTS IN LESS THAN STANDARD SEPARATION AND AN AMENDED CLRNC TO MAINTAIN VISUAL SEPARATION.

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WHILE ON A RADAR VECTOR DEP FROM VNY OUR TURBO JET WAS ASSIGNED AN INITIAL ALT OF 4000' MSL. 1000' PRIOR TO LEVEL OFF (3000') WHILE IN A TURN TO A HDG OF APPROX 255 DEGS WE RECEIVED A TFC ADVISORY AT OUR 10 O'CLOCK POS; 5000' MSL; SMT. BOTH CREW MEMBERS ATTN WAS MOMENTARILY DIVERTED LOOKING FOR TFC. I HEARD OUR ALT HORN. I (AS SIC) WAS ABOUT TO CALL '1000' TO GO WHEN I NOTED (ALONG WITH THE PIC) WE WERE 300' HIGH (4300'). AS SIC I WAS COMMUNICATING WITH BUR APCH AND HAD NOT HEARD THE FIRST ALT HORN FOR THE '1000' TO GO CALLOUT. I CALLED TFC IN SIGHT. BUR ADVISED OUR ACFT TO MAINTAIN VISUAL SEP AND CLB TO 8000' MSL. THE CTLR ADVISED US OF BEING ABOVE 4000' AND HAD A READOUT ON US OF 4400' MSL. WE ACKNOWLEDGED AND CONTINUED OUR CLB. AT 7000' MSL TFC WAS RPTED AT 2 O'CLOCK; 9000' (TYPE NOT KNOWN). AGAIN I LOOKED TO IDENT THE ACFT VISUALLY; HEARD AN ALT HORN; WENT TO CALL '1000' TO GO AND AGAIN WE WERE 300' HIGH AT 8300' MSL. APPARENTLY COMS DURING THE EARLY HORN WARNING WASN'T HEARD BY ME DUE TO CTLR COMS ABOVE THE TFC ADVISORY. THE REST OF THE FLT WAS UNEVENTFUL. IN BOTH CASES; FLYING IN A HIGH DENSITY TFC AREA; ATTN WAS DIVERTED LOOKING FOR TFC BY THE FLT CREW AND SUBSEQUENTLY MISSED LEVEL OFF ASSIGNMENTS. A SUGGESTION COULD BE FOR ATC DURING AN ACFT CLB; WHEN ISSUING A TFC ADVISORY TO ALSO RESTATE ASSIGNED ALT AS A REMINDER. THIS WOULD BE HELPFUL WHEN ATTN OF THE FLT CREW IS DIVERTED TO LOOK FOR TFC.