Help housing ~30 cats

I'm helping a family friend move and part of this process is going to require rehoming about 30 cats that are currently in the property with him. All the cats are taken care of, most live indoors, they've just proliferated and I offered to help him find homes for them before moving. There's quite a few litters of kittens in the mix as well.

I've called about 20 local organizations, foundations, Humane Society, etc. and not a single one is able to take ANY of the cats.

Any suggestions?