KING AIR 200 CAPT CONTINUES TKOF AFTER TWR CTLR AMENDED TKOF CLRNC TO TAXI ACROSS AND EXIT RWY DUE TO LNDG TFC BECAUSE TKOF ROLL HAD COMMENCED; TWR SENT THE OTHER ACFT AROUND.

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THE EVENT BEGAN AT WESTCHESTER COUNTY ARPT; WHITE PLAINS; NY; WHILE AWAITING AN IFR RELEASE AND TKOF CLRNC FOR AN IFR FLT TO NIAGARA FALLS; NY. I WAS THE PIC; HANDLING COMS AND NAV; ALONG WITH A COPLT; WHO WAS THE PF FOR THIS TRIP. THE WX WAS VFR; ALTHOUGH TSTMS WERE APCHING RAPIDLY FROM THE NW. WE WERE #1 FOR DEP; HOLDING SHORT OF RWY 34. SIMULTANEOUS RWY OPS WERE IN USE WITH TFC LNDG AND DEPARTING RWYS 34 AND 29. THE TWR CTLR WAS VERY BUSY HANDLING NUMEROUS INBOUND AIRLINE AND GA ACFT. WE WERE TOLD TO HOLD SHORT OF RWY 34 IN THE RUN-UP PAD ADJACENT TO TXWY L; AWAITING IFR RELEASE. AFTER APPROX 10 MINS; WE WERE TOLD THAT OUR RELEASE WAS RECEIVED AND TO CONTACT TWR. I CONTACTED TWR ADVISING THAT WE WERE READY FOR TKOF RWY 34. WE WERE TOLD TO HOLD SHORT FOR LNDG TFC; WHICH WE DID. AFTER THE NEXT ACFT LANDED AND CLRED THE RWY WE WERE INSTRUCTED BY THE TWR CTLR; 'ACFT X CLRED FOR IMMEDIATE TKOF; KEEP IT ROLLING; TFC ON A 2 MI FINAL.' I REPLIED; 'ACR X CLRED FOR TKOF; WE'LL KEEP IT ROLLING.' JUST AS WE WERE LINING UP ON THE CTRLINE OF THE RWY; THE CTLR SAID AGAIN; 'ACFT X KEEP IT ROLLING; TFC ON SHORT FINAL.' I REPLIED; 'ACFT X IS ROLLING.' AS THE COPLT ADVANCED THE PWR LEVERS TO TKOF PWR AND THE ACFT BEGAN TO ACCELERATE THE CTLR ANNOUNCED; 'ACFT X TAXI ACROSS AND EXIT THE RWY AND HOLD ON THE OPPOSITE TXWY.' BY THIS POINT THE ACFT WAS ALREADY ROLLING AND ACCELERATING RAPIDLY. I REPLIED; 'ACFT X IS ON TKOF ROLL; UNABLE.' RECEIVING NO REPLY I ANNOUNCED AGAIN; 'ACFT X IS ON TKOF ROLL; ADVISE.' THE NEXT RESPONSE I HEARD FROM THE CTLR WAS INSTRUCTING A COMMUTER AIRLINE FLT TO GO AROUND. WE CONTINUED OUR TKOF WHICH WAS EXECUTED WITHOUT INCIDENT. I FEEL A LARGE CONTRIBUTING FACTOR TO THIS SIT WAS THE HIGH WORKLOAD FOR THE TWR AIR TFC CTLR. HANDLING NUMEROUS INBOUND AND OUTBOUND ACFT; WITH SEVERE WX APCHING THE AREA; WAS VERY HECTIC AND THERE SEEMED TO BE SOME CONFUSION ON BOTH GND AND TWR FREQS AS TO THE POS OF SEVERAL ACFT. MY FIRST IMPRESSION WHEN GIVEN THE TAXI CLR INSTRUCTION WAS THAT THE CTLR MAY HAVE CONFUSED OUR ACFT 'N' NUMBER WITH SOME OTHER ACFT'S. IN ADDITION I FEEL THE CTLR SHOULD NOT HAVE ISSUED THE INITIAL TKOF CLRNC IN SUCH A MANNER; ESPECIALLY KNOWING THE SPD AND DISTANCE OF THE APCHING COMMUTER AIRLINE ACFT.