In a saga, can you have a new player jump in? Or is that considered illegal? I play two-handed and am thinking of adding 3rd for certain quest.

The campaign mode doesn't planned this. Illegal seem a little harsh but there is no way to do it in the rules.

Technically, you are not switching heroes, so you wouldn't incur the +1 threat penalty. There really isn't anything in the rules about this, so I would say go for it; especially if you're playing strictly thematically and have a limited set of "legal" heroes for one quest but at some point (Council of Elrond maybe) new heroes become thematically "available."

Thematically the number of players really *should* vary during the saga. Going from one player to two player (or three player) at the point of the Council of Elrond would be most fitting. Since there's nothing in the rules to prohibit it, no reason not to do so. Reducing the number of players should also be possible, any threat penalty from the removed heroes would apply to the no-longer existent player. However, the new player would miss out on any permanent boons (and non-encounter deck burdens) that they could have earned on previous quests.