NMAC BTWN A DEP B757 AND UNIDENTED TFC; SUPPOSEDLY A HELI; OFF THE DEP RWY AT 1500 FT AT MDPP; FO.

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DURING TAXI OUT AT MDPP; WE NOTICED WHAT APPEARED TO BE HELI TFC OVER THE RWY AT 1500 FT ON THE TCASII. THE WX WAS BROKEN CEILING; SO WE WERE UNABLE TO VERIFY VISUALLY. SINCE THE TFC APPEARED TO BE ALMOST STATIONARY; WE CONCLUDED THAT IT WAS A HELI. PRIOR TO BEGINNING OUR TKOF ROLL; WE VERIFIED THAT THERE WAS NO CONFLICTING TFC EITHER VISUALLY OR ON TCASII. AFTER I SELECTED WHEELS UP FOR THE FLYING FO; I LOOKED DOWN AT THE TCASII SCREEN AND SAW THE TFC THAT HAD DISAPPEARED PREVIOUSLY -- ONCE AGAIN IN OUR OVERHEAD POS AT 1500 FT. WE BEGAN A PUSH-OVER COMMENCING AT AROUND 700 FT AND PASSED 400 FT BELOW THE TFC. THE TCASII GAVE US NO TA'S DUE TO THE BUILT-IN INHIBITS. WE NEVER VISUALLY ACQUIRED THE TFC DUE TO THE CLOUD DECK; AND AFTER WE CLRED HIM; WE SAW THE TOP OF THE CLOUD DECK AT 1400 FT AND BASES AT AROUND 1000 FT. WE QUERIED THE TWR ABOUT THE TFC; AND HE HAD NO KNOWLEDGE OF HIS PRESENCE. IT WAS ONLY DUE TO A RE-CHK OF THE TCASII SCREEN AND TAKING IMMEDIATE ACTION THAT WE AVOIDED WHAT I AM SURE WOULD HAVE BEEN A MID-AIR COLLISION. THE TWR AT MDPP SAID THAT THEY WOULD INVESTIGATE WHAT THE TFC WAS THERE FOR AND TRY TO LOCATE HIM. MY FO DID A SUPERB JOB IN CTLING THE ACFT IN A DANGEROUS AND SPONTANEOUS SIT. THERE WERE NO INJURIES NOR WERE THE PAX AT ANY TIME AWARE OF THE INCIDENT.