ACR X UNAUTH CLB THROUGH OCCUPIED ALT HAD LTSS FROM ACR Y. SYS ERROR. PLTDEV. ACRS X AND Y NON COMPLIANCE WITH TCASII RA INSTRUCTIONS.

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LOW SIDE CTLR ISSUE CLB CLRNC TO FL230. ACR X READBACK FL280. LOW CTLR SWITCHED THE ACFT TO MY FREQ (HIGH CTLR). THE PLT CHKED ON CLBING TO FL280 WITH FL230 IN THE DATA BLOCK. I DID NOT HEAR. ACR X ASSIGNED ALT DURING CHK-IN. I THOUGHT ACR X WAS ONLY CLBING TO FL230. I ADVISED HIM TO EXPECT HIGHER ALT SHORTLY DUE TO SBOUND TFC. THE ACFT CLBED THROUGH FL230 AND NEARLY COLLIDED WITH SBOUND ACR Y AT FL240. SUPPLEMENTAL INFO FROM ACN 247499: ON TKOF FROM JAX WE WERE CLBING THROUGH 15000 FT AND TOLD TO CONTACT ZJX ON 132.3 MHZ. UPON INITIAL CONTACT WITH CTR; WE WERE CLRED TO FL280 AND I RESPONDED ROGER; ACR X CLRED TO FL280 AND SET FL280 IN MODE CTL PANEL. SINCE THIS WAS A SHORT LEG; I ASKED FO TO DO PA OUT OF FL180. FO HEARD CLRNC TO FL280 AND OBSERVED ME SETTING ALT IN MODE CTL PANEL. IN ADDITION; WE HAD A FLT INSTRUCTOR RIDING IN JUMP SEAT WITH NO HEADSET ON AND HE WITNESSED ME RESPONDING FL280 AND SETTING FL280 IN MODE CTL PANEL. WE WERE THEN CLRED TO 'NEW' CTR FREQ AND WHEN I CHKED IN; I ADVISED WE WERE CLBING TO FL280. APCHING FL270; WE NOTICED ACR Y ON OUR R FRONT QUARTER (1-2 O'CLOCK). ACR Y WAS NOT MOVING IN THE WINDOW -- NOT SURE IF ON PARALLEL COURSE OR COLLISION COURSE -- WITHIN SECONDS IT WAS OBVIOUS TO ALL OF US WE WERE ON COLLISION COURSE -- AT THIS MOMENT; WE RECEIVED AMBER TA ALERT (40 SECONDS UNTIL COLLISION) AT APPROX 6 MI. JUST PRIOR TO NEAR MISS; THE CTLR SAID; 'VERIFY YOU ARE AT FL230.' AND WE PROCEEDED WITH FLYING ACFT TO AVOID A DIRECT HIT. WE DSNDED AND ACR Y BANKED TO L AND PASSED BEHIND US. SUPPLEMENTAL INFO FROM ACN 247706: WE GOT A TA ON THE TCASII (WE NEVER DID GET AN RA) AND THE ATC CTLR CALLED TO CONFIRM WE WERE LEVEL AT FL230. THE CAPT WHO WAS FLYING; STARTED TO DSND AND ACR Y BANKED L TO PASS BEHIND US. SUBSEQUENTLY WE FOUND WE HAD BEEN CLRED TO FL230 AND WE READ BACK FL280. SUPPLEMENTAL INFO FROM ACN 247516: ACR Y ALERTED TO ACR X BY TCASII 'TFC; TFC' ON THE 30 NM RANGE. WE VISUALLY LOCATED THE TFC AND NOTED ITS DISPLAY AS MINUS 1100 FT AND CLBING. I SELECTED THE 10 NM RANGE AND NOTED THE ACFT AT 5 NM AND MINUS 800 FT AND STILL CLBING. COINCIDENTALLY; ATC CHALLENGED ACR X; 'ARE YOU LEVEL AT 230?' X REPLIED; 'WE'RE CLRED TO 280.' BY THIS POINT X HAD FLOWN THROUGH TO 243 BUT STARTED A DSCNT. I DECIDED TO EVADE BECAUSE COLLISION WAS IMMINENT. I BANKED 60 DEGS L AND ALLOWED THE NOSE TO DROP. AFTER A HDG CHANGE OF APPROX 45 DEGS AND A DSCNT OF APPROX 400 FT; I LEVELED THE ACFT; CHKED FOR CLRNC; THEN RETURNED TO OUR 210 DEGS COURSE; AND CLBED TO 240. DURING THE MANEUVER ATC CALLED X TO DSND TO 230. X RESPONDED; 'WE'RE NOW LEVEL AT 230.' ATC ALSO CALLED US TO RPT THE X TFC. WE RESPONDED. 'TFC IN SIGHT; WE'VE DEVIATED TO THE L TO AVOID THE TFC.' FROM THAT POINT ATC DEALT WITH X AND APOLOGIZED TO US FOR THE MIXUP. THE INCIDENT PROBABLY TOOK APPROX 45 SECONDS; START TO FINISH. TCASII PROVIDED FIRST ALERT; BUT BECAUSE OF THE CLOSURE RATE AND VISUAL CONTACT WITH X; EVASIVE ACTION WAS BEGUN BEFORE TCASII RESOLUTION WAS ACTIVE. AN RA WAS ISSUED DURING MY MANEUVER; BUT I DID NOT FOLLOW IT. IT WAS TOO LATE TO AVOID COLLISION; AND I WAS IN A TURNING MANEUVER TO AVOID A COLLISION. NO PASSENGER INJURIES. THE SEAT BELT SIGN WAS OFF. REQUIRED PA'S WERE MADE. CLOSEST POINT OF APCH WAS 900 FT LATERALLY.