PARALLEL VISUAL APCHS CAUSE BARRAGE OF TCASII COMMANDS.

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ON VISUAL TO RWY 28L AT SFO. ABOUT 15 MI OUT (NEAR MENLO) WE WERE TOLD WE WOULD BE ALONG SIDE AN LTT; PRESENTLY ON DOWNWIND; CALL IN SIGHT. WE CALLED IN SIGHT; AS DID LTT. BOTH CLRED FOR RWY 28L AND RWY 28R; RESPECTIVELY. ON FINAL FROM BRIJJ OM; WE LOST SIGHT VISUALLY; BUT HAD TFC BEHIND US ON TCASII. DISPLAY LOOKED AS IF LTT WAS LINED UP FOR RWY 28L. TCASII WAS SCREAMING AT US ALL THE WAY DOWN; FIRST RED; THEN YELLOW EVERY FEW SECONDS. WHENEVER RED WE'D COMPLY WITH TCASII COMMANDS; THEN IT WOULD GO YELLOW AGAIN. WE TRIED REPEATEDLY TO QUERY SFO TWR ABOUT LTT'S LOCATION BUT COULDN'T GET A WORD IN EDGEWISE; BECAUSE TWR WAS RATTLING OFF COMMANDS WITHOUT PAUSE IN AN EFFORT TO SQUEEZE OUT DEPS OFF RWY 1L&R. FINALLY; WE LANDED WITHOUT INCIDENT; BUT WE NEVER WERE ABLE TO TELL TWR THAT WE'D LOST SIGHT OF LTT; NOR WERE WE ABLE TO FIND OUT IF LTT STILL HAD US IN SIGHT. UNNERVING. THE TWR SHOULD NOT XMIT CONTINUOUSLY WITHOUT ALLOWING TIME FOR RESPONSES; AND SHOULDN'T TRY TO SQUEEZE OUT SO MANY XING DEPS.