Cropping a section of a photograph would be a modification, but "modification" doesn't give you the right to commercially use someone else's copyrighted work.
There is an exception for "fair use," which includes "transformative uses," but cropping one person out of a portrait would probably not be considered transformative, nor would photoshopping a missing family member into a photo. In both cases, you're just going from use as a portrait to another use as a portrait.
The changes needed to achieve fair use are qualitative, not quantitative. They cannot be definitively measured in percentages or additions or subtractions; the question is whether you've transformed the picture into something new.
For an example, you may want to read Cariou v. Prince, 714 F.3d 694 (2d Cir. 2013), which involved a an artist "taking photographs and other images that others have produced and incorporating them into paintings and collages that he then presents, in a different context, as his own." In some cases, there were very large changes, and in others, the changes were relatively minimal.
The court said that some of the uses were definitely fair use, but it said others were too close to call and sent it back to a lower court to do more analysis.
For your purposes, though, the key takeaway is that transformative use goes further than making a "modification" and turns the original work into something new with a message meaningfully different than that of the original.