I dunno about the 7 limit.
I managed ten people. Basically, you have to break it down into two parties, the alpha party having all your main characters, and the beta party having an extra four. The point is to include several scenes that are beta party heavy, because in all likelihood, 2/3 of the speaking lines will be taken by the point you get party members 5-9. Party member 9 in this game was a bonus character, who made frequent appearances as party of the plot. Member 10? In order to have her extra, but also not just a silent extra character, I ended up working her into the game epilogue (as the main character's daughter).
I'd say with four person parties, the standard is 10.
4 main party.
4 second party.
1-2 bonus characters, which shouldn't be random extras but should actually be worked into the plot.
In order to have a large party, you also need to base attacks around character personality, since the beta team and bonus players are not likely to get enough screen time. Example: FF6 Setzer. We meet him for like 3 major scenes in game. His battle system? "Oh, he's a gambler." It's evident right from the Slot ability, the dice weapons, and probably his limit break.