Yes, you want to make sure you've unlocked the larger rooms via the handbook. After that you will have larger rooms to choose from intially, as well as bigger rooms later.
To get additional rooms/bigger rooms you need to visit the villager on a fresh day and talk to them about remodel/remaking their home. Remodel is to just move furniture and remake will allow you to make the rooms larger/add rooms etc. You can also move the house entirely to another plot or change the seasons, whatever you want. but you can also just leave it there and make the rooms bigger.