meyers66, it depends on your riding. I also happen to have a Bianchi Volpe. I have 32mm tires on it and also fenders. I haven't tested to see what width I can put on, but I suspect I could put on at least 35mm tires while keeping the fenders. With the fenders off, I could probably put even wider tires. My Volpe is from the mid 90's, so the geometry has probably changed a bit, but not necessarily the tire width tolerance.

Changing your wheels makes things convenient, but I'm pretty adept at changing tires, and I wouldn't bother with that expense. I'd prefer to get another bike. It's more fun.

I don't have an off road bike. One of these days, I'll get around to it. In the fall, I took a long trail ride with a bunch of guys. Some had road bikes, and some had off road bikes. All of them had wider tires than I did. I guess that means I'm OK with off road riding with a road bike and road tires. I could have done it with narrower tires, but I wouldn't have wanted to. This was on the Old Croton Aqueduct trail in NY state.