Fitting bigger wheels is always trial and error. Factors mentioned above like width of wheel, offset and width of tyre are important.
What suspension you have is a major factor - at standard ride height you could probably fit 20" wheels in but the lower you go, the more issues you'll have with the arches.
Also, the wheels may rub on the suspension. Whereas most spring/strut combos will be the same diameter, coilovers might be narrower - but even then, different brandsof coilover differ in diameter.
Regarding tyres, two tyres from different manufacturers can have exact the same spec, e.g. 195/45/16 but one might have a rounder profile making it easier to fit under the arches.
You might also find that having your arches rolled helps - or with kitted cars folk have been known to remove metal from the arch altogether.