The difference between your big and middle chainrings is already 12 teeth. I would not increase the size of the big ring only. You could probably increase all three rings by 2 teeth and still have good shifting. Or you could increase the big and middle leaving the smallest at 22, but the shifting might suffer some. I would not do it any other way.
Is it possible? Yes. A good idea? Not in my opinion.
A cassette starting with an 11 would make more sense.