FO'S RPT ON MULTIPLE RWY CHANGES WHILE RADAR VECTORED INTO LAX. A CTLR INSTIGATED MISSED APCH WAS MADE AND A CLRNC INTERP PROB AROSE; RESULTING IN A POSSIBLE HEADING TRACK DEV.

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ON APCH TO LAX EARLY AM. WX; OVERCAST LAYER; TOPS AT 2000 FT; VFR ABOVE. ON SADDE 6 ARR TO LAX AT FILMORE TOLD TO EXPECT ILS RWY 24R. CREW BRIEFED APCH. 5 MINS LATER TOLD TO EXPECT ILS RWY 25L. CREW BRIEFED APCH. 2 MINS LATER TOLD TO EXPECT ILS RWY 24R. AGAIN; CREW BRIEFED APCH. SOON THEREAFTER TOLD TO EXPECT ILS RWY 25L AGAIN. CREW BRIEFED APCH. ASSIGNED VECTOR TO INTERCEPT ILS RWY 25L AT 2500 FT. INTERCEPTED AND DSNDED AT GS INTERCEPT. AT APPROX 1800-2000 FT APCH CTL INSTRUCTED IMMEDIATE TURN TO 360 DEGS CLB TO 2000 FT; FOLLOWED MOMENTS LATER BY A R TURN TO 130 DEG VECTOR. CREW READ BACK ALL ALT AND HEADING ASSIGNMENTS AND COMPLIED. WHILE PASSING 360 DEGS CREW BEGAN TO QUESTION 130 DEG HDG AS THAT WOULD BE A VECTOR BACK INTO APCH TFC. CREW SLOWED RATE OF TURN AND TRIED TO CONTACT APCH. DUE TO HVY FREQ CONGESTION CONTACT WAS NOT MADE UNTIL HDG 100 DEGS. APCH NOW ASSIGNED L TO 030 DEGS AND CLB TO 2200 FT. CREW RECEIVED VECTORS TO ILS RWY 24R APCH TO LAND. ACFT WAS VFR AND HAD ALL APCHING TFC IN SIGHT DURING VECTORS. TO THIS DAY IT IS UNKNOWN WHETHER CREW WAS SWITCHED TO RWY 24R FOR THE 5TH TIME AND MISSED IT; OR APCH THOUGHT THEY HAD SWITCHED US AND ACTUALLY HAD NOT OR CREW LEFT IN WRONG FREQ (FOR RWY 25L WHEN CLRED TO RWY 24R). ALSO CONFUSION WITH 030 DEGS AND 130 DEG HDG BTWN CREW AND ATC AND THE DELAY FOR VERIFICATION COMPLICATED MATTERS. THIS SIT MAY HAVE BEEN AVOIDED WITH SEPARATE APCH FREQS FOR N AND S COMPLEXES AT LAX TO DECREASE FREQ SATURATION AND/OR BETTER PLANNING ON APCH SEQUENCING SO THAT EXCESSIVE RWY APCH SHIFTING DOES NOT OCCUR.