Well, the appearance of the set changed from episode to episode - door color changes, different items decorating the aft wall, sometimes a viewscreen and a food slot near the console and sometimes not. Either the engineers had way too much spare time, or then we are actually witnessing several different rooms.
Also, while the "locally relative" positioning of the room never changed much (because after the pilot, it was a fixed part of the main corridor set), we got conflicting data on the deck where the transporter might be located. In "Dagger of the Mind", not only does the transporter room have a rare circuit board thing on the back wall, but it also delivers Dr van Gelder to somewhere near Deck 14. Possibly a secondary hull location, as the transporter was supposed to be moving only cargo, and the holds are somewhere down there. Indeed, this unique room may be one of the cargo transporters of the ship - possibly with bigger sisters somewhere nearby. Or then there are no bigger transporter, but there are bigger shuttlecraft (as seen in TAS)...
It's true that the appearance of the transporter room did change quite a bit over time - but one could say the same thing about the Engineering deck - the show's creative personnel didn't have any qualms about adjusting sets to serve the needs of whatever script they were shooting that week. But I think "The Enemy Within" makes a pretty strong argument in favor of there only being one transporter room on the ship. There's no reason that the contamination from Fisher's uniform should have affected other disconnected transporter circuits. There are also many many script references to "the Transporter Room" instead of "Transporter Room One" or something similar as was done on TNG, VOY, etc. Of course, I know it's all educated guesswork since it's not as if we have the actual transporter circuit diagrams to study. And I realize that the constant script references to a single transporter room could have just been shorthand for a single preferred transporter room by the senior staff. But it seems clear to me that, at the time the show was produced and aired originally, that the intent always was for the ship to have a single transporter room, even though it doesn't really make sense for that to be the case.