I don't know of a way to edit the snap. However if it helps, when you have snapped a piece, and then hover over that piece with your mouse, you can click on the dots, symbolizing an important part of that piece, (a clip, a stud, a hole for a bar to fit in, etc.) and you can then rotate from that point. For example, you could rotate where two pieces connect at the stud, or if you have a ball in a joint, you could rotate one of the pieces from the joint. Thus keeping the two pieces snapped together, while one piece moves separate from it. Or if you hold ctrl and click on multiple pieces (highlighting them in red) you can move as one connected piece.