I’m on level 365 and running out of island space. Getting ready to purchase Summer House which appears..

Summer House is the last 3x3 building available at this time. You will receive more space (i.e. the next island) when you clear all the clouds off of Orchid Island. Be aware, that if you place too many low-flower items on your island you will run out of space. Once that happens, you'll have to replace low-flower items with high-flower items in order to keep progressing in the game, which takes many replays to get the necessary coins.