Sixteen is the maximum number of party members you can have at one time, including nongeneric characters (like Mustadio or Agrias), generic characters, and generic monsters.

However, the game always has a place for guest characters, so you can temporarily have up to eighteen in the inventory (I believe the most number of guests you ever get at any one time is two).

If you want to make room for every nongeneric character, you'll eventually have to dismiss some of your generic soldiers and monsters. My suggestion is do as many propositions and monster breeding/poaching as you can earlier in the game.