Yes! You could theoretically even have a town filled with one personality type if you really wanted.
The catch is that the game will try to give you random move-ins and campsite people who suit what types are missing/who you have less of
So to do a lot of one type, the best way is to get them from other people's towns.
You could have just one personality type in your town if you truly wished to but the game wouldn't give them to you "naturally". You'd have to adopt them from other players.