In addition to what Jack said, I also had a client recently where we installed a wireless router. Their house wasn't quite as big as your client's - "only" 11,000 sq. ft. Really, really big. We looked into getting an omni directional antenna. The one we looked at for the client was a 4 ft. high "stick" that attached to one of the router's antennas (you need a router where you can unscrew the existing one). You can either build a stand for the antenna or hang it from the ceiling. Our client wasn't interested in that, so we dropped it.
Here's the one we were looking at, but there are others (and of course I don't know where you live - I'm in the US):
Good luck.