A BE40 CLBING OFF TTN ON ASSIGNED HEADING HAD A TCASII RA ON AN UNKNOWN ACFT AT 2800 FT AND A TA ON ANOTHER ACFT AT 4000 FT IN THE SAME AREA. THE BE40 WAS ASSIGNED 3000 FT AND CLBED TO 3500FT IN RESPONSE TO THE RA AND THEN TO WHAT THEY THOUGHT WAS THEIR NEW ASSIGNED ALT OF 4000 FT. THE DEP CTLR SAID THEY WERE NOT CLRED TO 4000 FT AND THAT THERE WAS NOT ANY 2800 FT TFC. BOTH CREW MEMBERS OF THE BE40 SAID THERE WAS ON THEIR TCASII.

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AFTER TKOF FROM TRENTON ARPT; NJ; I WAS IN THE R SEAT OF BEECHJET. OUR TKOF CLRNC WAS RWY HEADING TO 2000 FT. WE WERE HANDED TO APCH CTL GOING THROUGH 1000 FT. AT CHK IN; APCH TOLD US TO CLB TO 3000 FT AND TURN R TO HDG 270 DEGS. AS WE MADE OUR TURN I COULD SEE 2 TARGETS APPEAR ON THE TCASII. THE CTLR TOLD US THAT THE TFC WAS 'NOT A FACTOR.' THE HDG OF 270 DEGS POINTED US DIRECTLY AT THE 2 TARGETS. ONE TARGET DISPLAYED 4000 FT AND THE OTHER DISPLAYED AN ALT OF 2800 FT +/-100 FT. BOTH TARGETS WERE INSIDE 5 MI. OUR AIRSPD WAS 200 KIAS AND THE TARGETS WERE CLOSING FAST. THE CTLR SOUNDED VERY BUSY. THE TCASII ANNOUNCED A TA AT ABOUT 3 MI AND I COULD SEE THAT AN RA WAS COMING UP SOON. I ANNOUNCED ON THE RADIO THAT WE HAD AN RA (AS THE TCASII ALERT CAME ON) AND THAT WE WERE CLBING TO 3500 FT. THE RESPONSE BY THE CTLR SOUNDED LIKE HE SAID THAT 3500 FT WAS OK -- GO TO 4000 FT. WE MAINTAINED 3500 FT UNTIL WE WERE SURE THAT WE WERE PAST THE 4000 FT TARGET ON OUR DISPLAY AND THEN CLBED TO 4000 FT. AS WE LEVELED OFF AT 4000 FT THE CTLR TOLD US THAT HE HAD NOT CLRED US TO 4000 FT; BUT TO STAY THERE ANYWAY. IF I HEARD THE CTLR WRONG -- IT PROBABLY WAS DUE TO THE NOISE INTERFERENCE OF THE ALERTS COMING FROM THE TCASII AND THE OTHER ACFT TRYING TO TALK ON THE RADIO. I'M NOT SURE IF THE TFC AT 2800 FT WAS UNDER APCH CTL AT THE TIME -- THE CTLR TALKED AND ACTED LIKE HE COULDN'T SEE THAT TFC. SUPPLEMENTAL INFO FROM ACN 383004: ACFT AT 4000 FT WAS TALKING TO PHL APCH ABOUT THIS 2800 FT ACFT AT THIS TIME. WE DID OUR EVASIVE ACTION AND CLBED TO 3500 FT BTWN BOTH ACFT VERTLY. MYSELF AND OTHER CREW MEMBER ADVISED PHL APCH OF OUR ACTIONS; AT WHICH TIME; WE HEARD PHL APCH INSTRUCT US TO CLB TO 4000 FT. AFTER LEVELING AT 4000 FT MSL; BEYOND HORIZLY OF CONFLICT; CTLR ASKED US AT WHAT ALT WE WERE AT. WE ADVISED HIM AT 4000 FT AND HE SAID WE WERE NOT CLRED TO 4000 FT. AT THIS TIME HE HANDED US OFF TO NEW YORK APCH. THERE SEEMED TO BE CONFUSION REF THE 2800 FT TFC. THE CTLR ADVISED US THERE WAS NOT 2800 FT TFC TO AVOID; BUT WE KNOW THERE WAS. THERE WAS ALOT OF CLUTTER (CHATTER ON COM FREQ 123.8) WHICH I BELIEVE ADDED TO THE CONFUSION.