Moving an item and all its motion Keyframes all at once

Lets say you have a still image keyframed to move across the screen from point a to point b over so many seconds via it's Center positions. But, you need it to move in the lower portion of the frame rather than the top as it is now.

Easy. Hold down Shift+Command and then (you'll see the cursor turn into a hand - without arrows) hold them down while clicking and dragging your image along with it's keyframe paths all together to a new location.

You may have to zoom out of the canvas a bit to see both ends of your keyframe path. It will set extra keyframes along the path but they shouldn't alter the motion.