My car is a 2013 Honda Crosstour

Increasing the height of a vehicle is going to affect the suspension system and this would affect the roadholding and driving comfort etc, not to mention voiding the warranty.

What do you expect to gain by only increasing front or rear?

If you goning to increase height, better to do it on all four. However, you have to be cautious and not raise it too much. Remeber you change the alignment geometry whenever you change ride height, so tire wear could be a problem if you raise it too much.
Also handling (as stated eariler) will be effected.
Call the dealership to see if they have had customers to ask about this before and to see if this will effet the vehicle warranty.