Biggest tire I can run on a 1964 plymouth valiant

I've got 255/60/15 on my 66 valiant but its tight , sometimes a rub going over a bump , no riders on the rear seat etc. I would think a 235-245/60/15 with the right backspacing would be the ticket using a stock 8-3/4 small bolt rear , mine are 15x8 wheels w/ 4-1/2" backspacing