How can you expansions besides the stars and compasses?

Only way to expand is to have the stars and compasses. If you are out of room on your island, you have too many low-flower decorations on your island. You'll need to replace then with high-flower decorations to continue advancing the game and get more stars and compasses.

I was in that situation. I sold thousands of flowers worth of "cheap stuff" and opened a lot of space. I bought expensive items. The down side is it stalled me in the game and I had to play open scenes over and over for 2 or 3 weeks but in the end I had a lot of open space.