Biggest tire I can run on a 1964 plymouth valiant

I sure don't, pretty sure they don't make one. It's the size you need to maximize your tire width, but like I said a 15x7" with a 4.5" backspace is not a standard Mopar size. If you want something you can put a dog dish on in a 15x7" with a 4.5" backspace you're probably in custom wheel territory.
Sounds good !

Thank you so much for your help. I greatly appreciate it.