Tomb of Annihilation has a price list of tame dinosaurs, and there are regular dinosaurs races in Port Nyanzaru. There are multiple pieces of artwork in Tomb of Annihilation that include people riding dinosaurs. Assuming that the party arrives in Port Nyanzaru with all characters size medium (eg not halflings). Tomb of Annihilation lists deinonychus, triceratops, and hadrosaur as purchasable mounts. How many characters can ride each of the different kinds of dinosaurs available for sale? This is similar to the situation where two size medium humanoids can ride a horse but only one can ride a donkey.
Looking in the monsters section of the adventure, the Deinonychus is listed as medium sized, making it inappropriate as a mount for a medium creature and usable only for halflings or similar.
The Hadrosaur entry lists it as a Large creature with Strength 15 (slightly weaker than a riding horse), which gives it a carrying capacity of 550 lbs, likely enough to carry two medium creatures and their most important gear with little trouble. The DM will be the ultimate arbiter of how many creatures can sit on the back of a hadrosaur, but from a weight perspective there seems no reason to claim you couldn't have a second character riding pillion. (Most real-life hadrosaurs were quite big and probably push the boundaries of the Large size category, so I'd be inclined to be permissive on this front.)
The triceratops in the Monster Manual is listed as Huge beast with a massive 22 Strength (exactly the same as the elephant from the same book), giving it a carrying capacity of over 1,300 lbs. With a proper harness (likely some sort of howdah), one triceratops could probably carry your entire party! Space may be the limiting factor more than weight capacity here, so again it's going to be up to the DM to decide how that's going to work.
As many as the DM allows
(Subject to carrying capacity)
The rules state:
A willing creature that is at least one size larger than you and that has an appropriate anatomy can serve as a mount, using the following rules.
The “following rules” clearly only anticipate one rider per mount but they don’t expressly outlaw more.
If your DM decides that means one, then one it is. If they decide as many as there are angels on the head of a pin, then it’s that many.