Ok... i know you are using wrong word there... there isn't a GC house, GC are the city-state, main story of Eorzea, for player-run we use FC instead
If you are talking about the Grand Companies (Limsa's The Maelstrom, Gridania's Order of the Twin Adders and Ul'Dah's The Immortal Flames) then yes, you are able to make a switch to another Grand Company loosing your progress(maybe can't remember) of your previous pledge Grand Company.
You cannot MAKE a GC, but you can make a FC instead
For Free Company which i think is what you really "meant" here. Will be able to buy land for housing from respective GC(? need clarification here lol xD)