In Binding of Isaac: Rebirth was added a local Co-Op mode to up 4 players in total.
Those 3 extra player are not equal to the main player. Their appearance resembles a phantom in most skins.
A condition to add one of the Co-Op Players is that the main character must have at least one and a half hearts, giving the half to the extra player and remaining with one.
Another disadvantage is that in large rooms they are dragged by the camera as this moves with the main player.