The question of maximum number never really arose, but it's remarkable that we never saw more than six people beamed at a time. Indeed, in "The Apple", it appears that at first, six people beam down, and only then do three more appear - and no explicit story logic is provided for why the latter three (McCoy and two guards) would have opted to be delayed.
On the other hand, the number of pads on the transporter platform doesn't seem to be closely related to what is being transported, considering that people and objects may extend past the limits of a pad or cover several of them (say, when lying down injured). Which makes for an odd contrast with "Where No Man Has Gone Before" where the unconscious Gary Mitchell is deliberately held standing upright within the supposed "confines" of a single pad, and our other two characters pull their supporting hands away for the duration of the transport! Such a weird maneuver would seem to require pretty pressing reasons, which are never given.
On a separate issue, the ship probably had several of those six-pad transporters, as the single set underwent modifications that more or less force us to assume it represented several separate spaces. Moreover, the transporter was indicated to be on different parts of the ship in different episodes - for example in "Dagger of the Mind" it brings van Gelder to the lower levels rather than to the more familiar saucer Deck Seven. But perhaps only one platform could send its signal down to the target planet at a time, explaining "The Apple"? Certainly some transporter resources were bottlenecks and single points of failure, as seen in "The Enemy Within"...
I have the official blueprints to the Enterprise D and indeed there are multiple transporter rooms, and also multiple cargo transporters as well, and multiple holodecks as well. The holodecks have built in replicators as well, so if someone eats something that came from the holodeck, it was real food he ate, same reason why Wesley Crusher fell into the pond on the holodeck in the first episode, and was still wet when he stepped out of the Holodeck.
Another interesting thing is there are tanks for dolphins on the lower decks of the Enterprise even though they weren't seen in the series. Also this ship has a Captain's Yacht, which was never used during the Next Generation series. The Enterprise E version of that Yacht was used in the subsequent movies.