Yes, but how BIG ?
That depends on how big you are

Don't buy something that is hard for you to carry around and control while you are running from corner to corner. It may be better to buy smaller (medium) sized ones than a big one.

Fighting small fires with it means standing in place ( almost ) but fighting a live ( 2-legged or 4-legged ) creature with it could mean jumping here and there while holding it with ONE hand. A really big fire extinuisher may be too much to carry in a confrontation (unless you carry it on one of those foldable luggage carriers, but even them you will have maneuverability problems).

Besides, when you have two medium sized fire extiunguishers instead of a BIG one, that gives you several options like you and your roommate each carries one of them, or you use one and then may lose one battle, retreat to the next room, pull the other one and start another battle.