Don't know if anyone can help

[prodigy1]

My grandma sadly passed away 1st august I've ended up with her cat I already have 3 children and 2 dogs of my own and I possibly cannot house another pet, I've been ringing loads of animal shelters and all are full what can I do?

I would also like to say I've asked friends if they want to keep the cat I've asked some of my grandmas friends would they like to take in the cat and no luck!