Would it remain 4x or would it go even higher?
4(super-effective damage) X 1.25(Dry Skin) = 5
It is possible for a move to do over 4x damage in certain circumstances, for example the use of Forest's Curse, which adds a Grass typing.
An example of this is Escavalier, who under the effect of Forest's Curse takes 8x damage from Fire type moves:
4(original super-effective damage) X 2 = 8