POSSIBLE NMACS OR POTENTIAL CONFLICTS NEAR DEST ARPT. ALTDEV ALT EXCURSION.

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WHILE BEING VECTORED; WE HAD 3 RA'S ON TCASII; ALL WITHIN ABOUT 25 MI OF THE ARPT AND WITHIN 15 MINS OF EACH OTHER. THE 1ST OCCURRED AT 3000 FT MSL AND WE HAD TO CLB TO 4000 FT BEFORE 'CLR-OF-CONFLICT.' THE FREQ WE WERE ON WAS 126.4. THE OTHER 2 INCIDENTS OCCURRED CLOSER IN TO THE ARPT. AT NO TIME DID THE CTLR POINT OUT TO US ANY OF THIS TFC; NOR DID HE MAKE ANY ATTEMPT TO VECTOR US AWAY FROM THIS TFC. THE WX WAS CLR AND NICE WITH LOTS OF VFR TFC AROUND AND WE WERE VERY BUSY WATCHING ALL OF IT ON TCASII. I THINK THE CTLR WAS EXTREMELY BUSY TOO AND OVERLOADED. HE DIDN'T SEEM TO BE ABLE TO HANDLE IT ALL -- ESPECIALLY AFTER WE TOLD HIM ABOUT OUR 1ST INCIDENT. THIS WHOLE SCENARIO WAS PRETTY UNSETTLING FOR US -- WE FELT COMPLETELY ON OUR OWN; AND THAT HE WAS UNABLE TO CTL WHAT WAS IN HIS AIRSPACE. HE PROBABLY WAS DOING HIS BEST; BUT MORE CTLRS WORKING THAT AREA WOULD DEFINITELY HELP INCREASE THE SAFETY LEVEL. SUPPLEMENTAL INFO FROM ACN 272356: (IT WAS LIKE FLYING INTO A COMBAT ZONE.) WHILE THE CTLR DID ATTEMPT TO POINT OUT SOME TFC; BUT MADE NO MOVE TO VECTOR AROUND; WE NEVER CALLED OUT HAVING A VISUAL IN MY TFC. I SINCERELY BELIEVE VFR TFC AND IFR TFC NEED TO BE SEPARATED. MORE POSITIVE CTLED AIRSPACE IS NEED FOR JET ACFT.