As mentioned. As of Relics, there are only five Federation Starships named Enterprise.
This gives two places of wiggle room.
A. That there are other ships named Enterprise that aren't registered under "Federation"...just as an Earth ship, or a Vulcan ship, or a Trill ship, that is registered for that planet and not the Federation...which implies it is used by Starfleet for the whole of the Federation.
B. There are other vessels named Enterprise that are not classified as Starships. This is an odd one as for a long time the term "starship" would seem to imply a specific and special kind of spacecraft. Later that might have become generic if a runabout is considered a starship (which I don't recall if that was the case or not).
The three bit of wiggle room is if an other ship that was named Enterprise was recommissioned at some later date and used in the fleet. It is still considered part of the original five Federation starships listed by the computer, but doesn't mean they all served in a linear order. Such as the Enterprise-A, or Enterprise-B being reactivated following the destruction of Enterprise-C until such time as the Enterprise-D was officially named (this requiring the older ship to be decommissioned, or renamed to free up the name).
That Starfleet does not seem to be extremely ridged on the idea that two ships can't have the same name at the same time (see USS Melbourne) does mean that it is possible for two Enterprises to be in service at the same time, if briefly, without needing to decommission one prior to the launch of the next. Though that might have been the reason for Enterprise-A's decommissioning...the imamate commissioning of Enterprise-B. Was the ship kept in mothballs, was is scrapped? Did Kirk blow it up like Shatner's novels have it? Was it renamed to give the name to the -B and then recommissioned for service, if one assumes it is a relatively new ship after Star Trek IV?
Was the Enterprise-A rebuilt to match the original's configuration during the Five Year Mission under Kirk and registered as NCC-1701-M?
Lots of odd questions. No answers.
But here is something off the wall to speculate on.
In Relics, it is clear that Scotty thinks Kirk might have brought the Enterprise-A out of mothballs to come get him. Clearly this isn't possible due to Kirk's death on the Enterprise-B which Scotty witnessed.
But, what if it is possible? Lets take something out of both TNG and the NuTrek films. Spock gives Scott the final piece of his transwarp beaming formula. When did Scott prefect that? He was clearly working on it at a much younger age in the NuTrek films, yet we never hear about it before. Now think of Relics. As a last ditch move to survive, Scott and Franklin use the transporter as a stasis chamber. But, what if that wasn't the first thing they tried. What if Scott tried transwarp beaming first, and it half worked?
I've lost you now, right? Now think about what happened to Will Riker. He has a transporter accident that split him into to identical people, yet they didn't know of the other's existence, nor were they the split person that happened to Kirk a century earlier. Now, what if this happened to Scott and Franklin? The crew of Enterprise-D seemed surprised to find Scott on this transport. Maybe because as far as they know he lived beyond that point.
Think of Star Trek VI. Scott says he just bought a boat. Perhaps immediately after the Enterprise-A is decommissioned, Scotty get on a transport to the Norpin colony. It hits the Dyson sphere, kills most of the crew. Scott uses his untested transwarp beaming setup to beam himself and Franklin to Earth. He is successful, and both Scott and Franklin live on. Scott logs the formula for transwarp beaming, which is immediately locked down by Section 31, as is all mention of the Dyson Sphere. Scott tells Spock about the formula on the side just to spite the Section 31 tossers. Scott later goes to the commissioning ceremony for Enterprise-B and witnesses Kirk's "death". Scotty dies at some point due to old age in retirement.
However, the interference from the Dyson Sphere also bounced back a copy of Scott and Franklin. That Scott thinks he failed and then comes up with the stasis method as a last chance. The duplicate Scott survived some 75 years later, but the duplicate Franklin does not. This Scott doesn't know that transwarp beaming is possible, but possibly works on it again later on, perhaps running into Spock again.
But via these methods, you have three things done:
A. Two Scotts that can follow the on screen canon.
B. A Prime universe example of transwarp beaming that would be sequestered.
C. A possible way to hide the Dyson Sphere from the record books even though it should be on a relatively common warp lane between Earth and Norpin Colony.
