We know from "Journey to Babel" that it's possible to order "photon torpedoes 2, 4 and 6" to be fired forward in a single volley. That sort of suggest that there are (at least) six forward tubes, although we could also postulate that a single tube fired the torps in quick succession. From "Elaan of Troyius" we know that forward torpedo tubes can be referred to in plural, though. And ENT "IaMD" establishes an aft tube, at least for NCC-1764 (which may be an upgunned model, though).
Having six ENT-style tubes would be rather logical for the TOS ship, I guess.
Timo Saloniemi