FLC OF AN MLG TOOK EVASIVE ACTION AND STOPPED CLBING DURING DEP IN RESPONSE TO VISUAL SIGHTING OF OTHER TFC; TCASII RA; AND ARTCC CTLR TA. CTR CTLR ADVISED THAT THEY HAD NOT BEEN ASSIGNED A HIGHER ALT AND TO RETURN TO THE VACATED ALT.

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AFTER DEP FROM RST AND HANDED OFF TO ZMP; CLRNC WAS GIVEN TO CLB TO FL230. AS PNF; I ENTERED FL230 INTO THE ALT WINDOW. BOTH PLTS ACKNOWLEDGED THE ALT OF FL230 AND CONFIRMED THE PROPER ALT. PASSING FL210; THE CAPT (PF) SAID THAT HE WOULD MAKE AN ANNOUNCEMENT TO PAX OF THIS SCHEDULED FLT REPLACED BY ACR X. XFER CTL OF THE ACFT WAS THEN GIVEN TO ME. I ACKNOWLEDGED AS SAYING 'I HAVE THE ACFT.' THE CAPT WENT OFF COM WITH ATC TO HAVE A TALK TO THE PAX IN THE CABIN. PASSING FL217 ZMP ASKED FLT 'WHAT IS YOUR ALT?' I ACKNOWLEDGED BY SAYING; PASSING FL217 FOR FL230. SHE (ATC) SAID 'DSND TO FL210; I GAVE YOU FL210; TFC 12 O'CLOCK PASSING L TO R; MAINTAIN FL210.' AT THIS TIME THE CAPT; SEEING THE TFC AND HAVING VISUAL CONTACT; TOOK THE ACFT OFF AUTOPLT; MADE A L TURN VISUALLY. AT THIS TIME AN RA THROUGH TCASII WAS RECEIVED; 'TFC; TFC;' 'MONITOR VERT SPD;' 'MONITOR VERT SPD;' 'CLB; CLB.' THE CAPT CLBED TO FL226 BEFORE CLR OF CONFLICT WAS RECEIVED. I; PNF AT THIS TIME; CALLED ATC AND INFORMED THEM OF OUR TCASII RA. THEY ACKNOWLEDGED WITH CLB TO FL240 CONTACT ZMP. (GIVEN NEXT FREQ.) NOTHING FURTHER WAS SAID TO OR FROM ATC. FLT CONTINUED SAFETY WITHOUT INCIDENT. IT SHOULD BE NOTED THAT AT NO TIME DID FLT RECEIVE CLRNC TO FL210 -- AT LEAST AS A FINAL OR LEVELOFF ALT. THE LAST WE HEARD AND ACKNOWLEDGED WAS FL230. OUR CONFLICTING TFC WAS AT FL210 -- THE WRONG ALT FOR DIRECTION OF FLT. AT NO TIME WAS EITHER ACFT IN DANGER OF COLLISION. THE CONFLICTING TFC WAS IN VISUAL CONTACT BEFORE WE RECEIVED A TCASII WARNING AND ACTION TO AVOID THE TFC WAS TAKEN PRIOR TO THE RA. THE EQUIP PERFORMED CORRECTLY. BUT MORE IMPORTANTLY; THE PLTS PERFORMED WELL. TCASII IS NO REPLACEMENT FOR SEE AND AVOID.