Biggest front tire that can be run on 1964 plymouth valiant

One thing you will need to know when you start getting responses is the respondents wheel width and backspacing. The backspace or offset will determine where along the width of the rim it bolts to the axle so a given tire may work great on a wheel that maintains the stock outer track width but "wraps" around the drum or disc, whereas one with little backspace but wider than OEM will possibly rub on the fender, if that makes sense?

A quick internet search for backspace wheel and tire calculator will allow you to compare all kinds of wheel and tire combinations. I've done this on a couple builds and it can become quite the science project but well worth it in the end. Good luck.