Three's a little excessive, that'd be fifteen companions already based upon the EA classes so far, and the companions are all voiced. That's just not viable. At most it will be one per class with a variety of male and female characters that can be romanced.
Actually it'd be way more than that. There are 12-13 official classes, and one officially unofficial class. Assuming Bloodhunter will not be a thing, we will still have the following: Barbarian, Bard, Cleric, Druid, Fighter, Monk, Paladin, Ranger, Rogue, Sorcerer, Warlock, Wizard and maybe Artificer. Not having Artificer would mean 12 origin companions (one for each class) and 24 non-origin companions (2 for each class) for a total of 36. With artificer that would become 13 and 26 meaning 39 fully voiced companions.
And honestly, I would love for resources to go to this, and I have ideas on how Zarna's idea could work. In particular, you just make non-origins less complicated. They are fully voiced but not to the level of origin companions, they maybe have one quest instead of the overarching storyline Origins would have, and in general as characters they are more shallow. That said, I wouldn't want them to be generic, I mean more shallow like how half the cast of BG1 was pretty shallow and just had something iconic to them, like Tiax. In fact, this would be a great escalation to BG1's companion list as well as an opportunity to flesh out the world and add interesting stuff to it. You could have them as "quest rewards" or part of certain encounters like BG1, some could be a bit more complex and have a bit of a plot, and some could just be an opportunity to add someone wacky to the group, like the world dominator and ascending god Tiax.
I do realize it is a bit much though, perhaps excessive, but honestly, it feels like the ideal to me and could really push BG3 to be even greater, and it could be something that is slowly worked on over the course of the EA.