Despite this legendary status, however, transporters were not always as integral to the universe of Star Trek. Originally, transporters were introduced to Star Trek as a technical workaround for the fact that the special effects required to show the Enterprise landing on a planet were prohibitively expensive (a starship wouldn't be shown landing until Star Trek: Voyager). Since the transporters were originally more of a solution to a problem than a carefully developed plot element, it is hardly surprising that The Original Series did not, initially, get too specific about the placement of transporter rooms on the Enterprise.
Captain Kirk's Enterprise Had Multiple Transporter Rooms In Star Trek: The Original Series
It Makes Sense, And There's Evidence In Star Trek: The Animated Series
Although Captain Kirk mostly refers to "the transporter room," singular, in The Original Series, there is evidence that there were at least four separate transporter rooms on Kirk's Enterprise. For one thing, it just makes sense that there would be more than one transporter room on a ship the size of the Enterprise. At various points in The Original Series, the crew complement of the Enterprise is given at either 203 or 428, but with either number, it would make sense that the Enterprise would have multiple transporter rooms if only as a precaution for a potential evacuation.
If we want more concrete evidence for the specific number of transporter rooms on the Enterprise, the best place to look is actually Star Trek: The Animated Series. 15 minutes into "Mudd's Passion," Lt. M'Ress (Majel Barrett Roddenberry) says, "coordinates relayed to transporter room four," thus making it clear that there are at least four transporter rooms on the Enterprise. Small details, like food replicators that appear in transporter rooms in only some episodes of The Original Series, also suggest that there are multiple transporter rooms at work.
Star Trek Later Dropped The Idea Of Multiple Transporter Rooms (Sort Of)
It Turned Out The Number Of Transporters Wasn't That Important For TOS
Despite the fact that there is some evidence that there were more transporter rooms on the Enterprise, for the most part, characters on the show act like there is only one. So, although in some early episodes like "The Galileo Seven," Captain Kirk speaks about transporter rooms in the plural, for the rest of the show, it's framed as though there is just one room, or at least one main transporter room.
People call it "the transporter room," without clarifying a number, and there is never any confusion about which transporter room away teams are going to meet up. So, during Star Trek: The Original Series, it seems like showrunners never really wanted to hammer down the exact number of transporter rooms on the Enterprise, instead leaving things up to the needs of individual episodes.
