A B737 FLT CREW EXPERIENCED A TCAS RA WHILE LEVELING OFF AT THEIR ASSIGNED ALT.

Narrative

CLBING OUT OF ZZZ1 GOING E; ATC GAVE US AN OFF-COURSE VECTOR DURING THE CLB; THEN A FEW MINS LATER BACK ON-COURSE AND CLB TO FL210. TCAS ADVISORY FOR TFC WAS RECEIVED IN THE CLB FOR TFC ABOVE US AND APPARENTLY IN TRANSIT TO POSSIBLY A LOWER ALT. WE HAD VISUAL SIGHTING OF THE ACFT. OUR ACFT WAS ON AUTOPLT BUT CLBING RAPIDLY DUE TO A LIGHT LOAD. AROUND FL205 THE MCP ALT ACQUIRED MODE ENGAGED FOLLOWED SHORTLY BY A TCAS RA TO ADJUST VERT SPD. THE AUTOPLT WAS ALREADY LEVELING AT FL210 SO I LET IT CONTINUE THE LEVELOFF AT THE ASSIGNED ALT OF FL210. WE DID NOT EXCEED OR OVERSHOOT THE ALT; BUT THE ACFT ABOVE US RECEIVED AN RA AND IT CLBED UP INTO THE PATH OF ANOTHER ACFT. IT SEEMS THAT THE XING OF 3 ACFT AT 3 DIFFERENT ALTS AT JUST THIS MOMENT WAS THE CAUSE OF THIS ONE. ABOUT 5 MINS OR SO LATER; ON ANOTHER ZZZ FREQ; THE ATC CTLR ASKED US IF WE HAD BEEN LEVEL AT THE ASSIGNED ALT OF FL210. THE FO CONFIRMED IT. ALL ACFT WERE ASSIGNED ALTS IN A CLOSE APPROXIMATION TO EACH OTHER. NORMALLY THERE WOULD PROBABLY HAVE NOT BEEN A PROB; BUT I THINK OUR HIGHER THAN NORMAL CLB RATE TRIGGERED THE TCAS SYS ON THE ACFT ABOVE US. ALTHOUGH NOTHING FROM MY VIEW WAS DONE INCORRECTLY; IT SEEMS THAT HAVING 3 ACFT CONVERGING WHILE IN TRANSITION COULD LEAD TO FUTURE PROBS.