Is it possible to increase the player board capacity by inviting additional players to a private game after creating? For example; if I create a private board with 2 players but after, invite 3 more before the games starts, would the player cap increase to 5?

Game was initially created for two, so that game will begin once second seat is filled, invites of more just becomes of field of potential candidates for that second seat. If you want a larger game you could just delete first game and begin again inviting more folks to a larger game.

Thanks for the clarification!