Side note:
The Chief Master at Arms of USS Inchon (back in 1993-ish) told me that they would practise firing Sea Sparrows at close targets by firing one missile and then firing the next when the first was at around 3/4 of the way to the target, and repeat that pattern, pointing the director at the next target as they were hit.
which supports the "as many missiles at the same target as you wish", I guess