MULTIPLE RWY OP INTERSECTING RWYS ACR X HAD NMAC LTSS FROM ACR Y AT INTXN OF RWYS. SYS ERROR.

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ACR X WAS TAXIING TO RWY 9L. ACR X REQUESTED NEW NUMBERS FOR MAX PWR RWY 9L -- ATC TWR TOLD US TO TAXI POS AND HOLD -- WE TOLD ATC WE WERE AWAITING NEW NUMBERS. ATC THEN DIRECTED US TO HOLD SHORT ON THE PAD AT RWY 9L. AS WE WERE ARRIVING ON THE PAD OUR NEW NUMBERS CAME UP OVER ACARS AND WE ADVISED ATC WE WERE READY. TWR THEN SAID 'AH -- ACR X (HESITATION) TAXI POS AND HOLD RWY 9L' -- WE ACKNOWLEDGED WITH 'POS AND HOLD RWY 9L ACR X.' WE COMPLETED OUR CHKLISTS AND WERE TURNING THE CORNER WHEN TWR INSTRUCTED 'RWY 9L CLRED FOR TKOF.' WE ACKNOWLEDGED AND STARTED TKOF ROLL -- JUST AFTER V1; WE NOTICED ANOTHER SAME COMPANY ACR Y RWY 32L ROLLING TOWARDS THE RWYS 32L/9L INTXN ON A COLLISION COURSE. CAPT COMMANDED FO TO 'GET IT UP' (FO'S LEG) AND WE PASSED DIRECTLY OVERHEAD ACR Y. AT 1000 FT AGL AFTER ACFT CLEANUP THE CAPT QUERIED THE CTLR ABOVE THE NEAR MISS. THE CTLR REPLIED 'OH I SEE THAT NOW IT WAS MY FAULT -- SORRY ABOUT THAT.' SUPPLEMENTAL INFO FROM ACN 213872: TAKING OFF RWY 32R ORD ANOTHER ACFT CLRED TO TKOF ON RWY 9L. APCHING INTXN NOTICED ACR X. ADVANCED THROTTLES TO FIREWALL CLRING INTXN. ACR X AIRBORNE ABOUT 2000-2500 FT FROM OUR POINT.