Short cage or long?
Short cage handles exactly what you currently have.
Long cage will handle exactly what you want.
Both max cog size and total chain wrap.

EDIT- I would venture to guess, you have a short cage.
Shimano is somewhat conservative in their ratings, but a 4T larger big cog may be a bit too much. It might be doable, but there are too many variables including RDER hangar geometry to tell until you try. If you have the GS version (longer cage) you would still need a longer chain.

If you are barely making it up the hill now, 4T more will be a godsend.