I think around the five-eighths mark (between halfway and three-quarters) tends to be Last Chance territory for adding a primary character that feels good narrative-wise (thinking about Harry Potter for instance, Luna Lovegood was the last character introduced that earned any real audience sentiment and she made her first major appearance around this point).
- A few people have mentioned that you can extend this limit a bit by giving the character a significant role in the story early on (or having them temporarily join your party early on).
From a gameplay perspective, if you have a limited number of spots in your active battle party, that's also something to consider. If your game's mechanics don't encourage frequently swapping around your active party, then there's going to be a point where the player feels comfortable with their party and team strategy (for me it's usually been when I have had 2 reserve members for a few hours of gameplay) and it's going to be difficult to convince most players to remove one of these characters that they like a lot in order to slot in the new one(s).
- Your own game's pace and mechanics will be what determines where the "last chance" point is, or if there is one at all. If those aren't working in your favor, however, one trick you could use to push the limit is to have a segment when the character joins where you have to use them for an hour or two, either by forcing them into your active battle party for plot reasons, or by splitting the party up into two so that there are no "reserve" members for a little while.
Finally, if your game has a significant postgame segment, adding a new character in the postgame can make for a compelling reason for the player to keep enjoying the game they've already beat. It also allows you to introduce classes that might be gamebreaking or simply too different to include during the "main" game - for example, I've designed a class for
How Badly that can transform into allies and enemies to copy their stats and moves, create enemies to aid in grinding, change the scope of spells, etc. I really liked these ideas, but I felt they would mess with battle strategy too much, so I'm adding them to a postgame character in order to offer it as a fun alternative for the player after they've completed the game the way it's "meant" to be played.
- The downside, of course, is that some players will stop playing once they complete the main narrative and the credits roll. Postgame characters work best when the game offers very compelling gameplay (read: the gameplay, not the story, is the main thing that keeps the player going) or when the game offers significant amounts of structured postgame content.