PA34 SUFFERS NMAC WITH PA31 DURING LNDG APCH AT FPR. EXTREME CONGESTION OF AIRSPACE AND TWR FREQ CONTRIBUTED.

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APCHING FPR FROM THE ESE; I WAS TOLD TO ENTER R DOWNWIND FOR RWY 9. THE TWR FREQ WAS VERY CONGESTED -- LOTS OF STUDENT TRAINING TFC. UPON ENTERING DOWNWIND; TWR ADVISED OTHER TFC ON DOWNWIND; AND OTHER TFC ON L DOWNWIND. I WAS GIVEN A LNDG SEQUENCE. PAST THE NUMBERS; STILL ON DOWNWIND; TWR ADVISED ME TO EXTEND DOWNWIND. I PASSED TFC (SAFE DISTANCE) ON FINAL. FREQ WAS VERY CONGESTED; AND I ATTEMPTED TO CALL TWR TO ASK FOR OK TO TURN BASE. I FINALLY GOT THROUGH TO TWR; AND THEY ADVISED OK TO TURN BASE; BUT I WAS THEN ABOUT 3 MI FROM (WEST OF) THE ARPT. I TURNED BASE; TURNED FINAL; KEPT SPD UP DUE TO DISTANCE FROM ARPT. I HEARD TWR TALKING TO A NAVAJO ON AN APCH TO RWY 9. TWR CLRED ME TO LAND. A THIRD ACFT RADIOED THAT 'THOSE 2 ACFT ARE RIGHT ON TOP OF EACH OTHER.' TWR CALLED THE NAVAJO FOR THEIR POS. I SAW THE NAVAJO ABOVE ME ABOUT 50 FT (ON FINAL). TWR HAD ME MAKE A L 360 DEG TURN AND RE-ENTER PATTERN. I HEARD TWR ASK THE NAVAJO WHY THEY DIDN'T RPT 'MARKER INBOUND.' LATER; ON THE GND; I SPOKE WITH THE NAVAJO PLT. HE STATED THAT HE NEVER SAW ME. MY THOUGHTS; VERY CONGESTED FREQ AND LOTS OF STUDENT ACTIVITY MADE IT HARD FOR ME (AND POSSIBLY THE NAVAJO PLT) TO 1) ADVISE TWR OF OUR LOCATION; AND 2) ASK FOR VERIFICATION/LOCATIONS. THE TWR CTLR MUST NOT HAVE BEEN WATCHING FINAL APCH; OTHERWISE; HE CERTAINLY WOULD HAVE SEEN 2 ACFT RIGHT ON TOP OF EACH OTHER. THIS IS THE THIRD TIME I'VE HAD A FRIGHTENING NEAR-MISS CLOSE TO FPR. I'M CONCERNED THAT A REAL ACCIDENT IS GOING TO HAPPEN SOON. MANY OF THE PLTS ON FREQ USED TO BE MORE TERSE IN THEIR COMS TO MINIMIZE CONGESTION. THE TWR CTLRS ARE WORKING VALIANTLY TO KEEP THE TFC FLOWING; BUT NEED TO BE WILLING TO HAVE ACFT WAIT RATHER THAN JAM SO MANY INTO THE PATTERN; AND KEEP A BETTER EYE ON TFC IN THE PATTERN. FPR IS THE FARTHEST N CUSTOMS' ARPT OF ENTRY -- THE ONLY REASON I LANDED AT FPR IS FOR THAT. I WISH THERE WERE MORE ARPT OF ENTRY OPTIONS; SO THAT I COULD AVOID THAT ARPT.