MOPED ARMY

you can go bigger. check how wide your fenders are. the swingarm can for sure fit a 2.5 with the fender on, and the fork could probably fit the same.

if you take the fenders off maybe you can fit 3s

i got 2.5 gazelles on my snowflakes. and yes, it was really hard, doable, but really hard.

you could relace a wider rim maybe?

You don't need wider rimes you can run any width tire from 2, 2.25, 2.5 or 2.75 on any Puch wheels, snowflakes, spokes or mags, doesn't matter. It might be a pain taking them on and off, especially with Cheng Shins or Gazelles. But thats not because they don't fit, its just because its hard to take them on and off.

The problem is the swingarm on a Maxi. It is hard to run anything larger than 2.25. I've seen people run 2.5 Savas (small for a 2.5 tire) on a Maxi but it always seems like the back tire is rubbing the swing arm. The front isn't a problem as long as you have fender clearance.

The way people usually run big tires on a Maxi is to replace the swing arm with one from a Magnum or a Freespirit, both bolt up and have enough clearance to run bigger tires.

You can run mismatched tires on a stock maxi as well, I've put a 2.5 in the front and a 2.25 in the back. (BMX bikes used to do this when I was a kid) Probably silly but a little more rotational mass in the front makes it feel smoother, easier to ride no-hands. And maybe there is a little less chance of having your front end wash out. Looks wise its hard to tell unless someone tells you.