FLC OF ADVTECH MLG PURPOSEFULLY CLBS PAST ALT ASSIGNMENT DUE TO TCASII RA.

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CLRNC WAS TO MAINTAIN 5000 FT ON SJC 7 DEP. WHILE IN TURN AT MAX CLB PWR GOING THROUGH 3700 FT; ATC INSTRUCTED US TO MAINTAIN 4000 FT. THE FO PUSHED THE NOSE OVER AND REDUCED PWR ABRUPTLY TO LEVEL OFF. TCASII THEN SAID 'TFC; TFC;' THEN 'CLB; CLB; CLB.' THE VSI SHOWED RED UP THROUGH APPROX 4000-6000 FPM. THE FO APPLIED MAX CLB PWR; INITIATED A CLB; AND THE INTRUDER BECAME VISUAL AT APPROX 4200 FT. I ADVISED ATC THAT WE WERE CLBING IN RESPONSE TO AN 'RA' AND HAD BUSTED OUR LAST ASSIGNED ALT. TCASII NEXT SAID 'MONITOR VERT SPD;' WE CONTINUED OUR CLB; AND AT THIS POINT ATC GAVE US AN UNRESTRICTED CLB TO FL230. (MUCH DISCUSSION OCCURRED WITH ATC DURING AND AFTER THIS EVENT.) AT APPROX 4700 FT TCASII SAID 'CLR OF CONFLICT.' THERE WAS DEFINITELY A CONFLICT AT 4000 FT. TCASII PROVIDED THE CORRECT ESCAPE PATH FOR THIS CONFLICT. THE FO DID AN EXEMPLARY JOB OF FLYING THE ACFT; WHILE TRYING TO FOLLOW THE INSTRUCTIONS OF MYSELF; TCASII; AND ATC; AND OBTAINING VISUAL CONTACT ON THE INTRUDER BEFORE I WAS ABLE TO (THE INTRUDER WAS ON HIS SIDE OF OUR ACFT). ATC DID NOT APPEAR TO HAVE ANY PROBLEM WITH OUR MANEUVERS; BUT SEEMED VERY CONCERNED WITH THE INTRUDER'S POS IN RELATION TO OURS. I BELIEVE IF WE COULD HAVE FLOWN DIRECTLY TO 5000 FT AS STATED IN OUR INITIAL CLRNC; WE WOULD HAVE HAD NO CONFLICT; BUT ATC SEEMED CONFUSED AS TO WHERE TO PUT US BECAUSE OF THE ALT READOUTS THEY WERE GETTING FROM THE INTRUDER. IN THIS CASE TCASII WORKED TO OUR ADVANTAGE; BUT WE DID BUST OUR REVISED CLRNC ALT; EVEN THOUGH WE REACTED IN ACCORDANCE WITH PRESCRIBED PROCS.