Hi and welcome to
Symi Chat.Perhaps if you gave us some idea of the kind of accommodation you are looking for we may be able to help. Do you want a hotel room? A self catering apartment? Or perhaps a house?
And will you be travelling independently or are you looking for suggestions for a package tour operator?
I have to say I'm surprised you're finding that all places are full already for dates in May next year, that's ages away!