In TAS, Kirk's TOS ship was finally seen firing apparent dorsal phasers in "One of Our Planets is Missing":
Make of that what you will; clearly this doesn't correspond to the TMP emitter locations, and some might argue that those bright dots are portholes. Then again, Franz Joseph once argued they were torpedo tubes...
But TOS "Paradise Syndrome" featured dialogue on four separate forward-firing phasers, fired in sequence. Two of these could be associated with the usual twin ventral firing location explicitly, a third probably; a fourth fired without exterior VFX to tell where it might have been located. Perhaps the dorsal emitter shown in TAS was the fourth bank?
TOS dialogue or walla also mentioned amidships and aft phasers, never seen firing. OTOH, no dialogue suggested that the ship would have been incapable of firing in some direction.