Hands draw and move in objects in, but they can also move the paper to make room for a new drawing side by side with the old drawing.

This can be used in a nuanced way - sort of pushing the paper a bit aside so drawing continues to its left or right - but also as an inter-cut between two scenes, with the drawing pushed completely out of sight and a new drawing then begins on a clean piece of paper.  

This kind of move is very typical for "cutout: type of animations.

This is all an extension of the current feature that slides an object on to the canvas instead of drawing it. This feature would enable a whole range of creative possibilities. Here's a wish list: 

1. A hand that slides the entire canvas 
2. A hand that slides one object around or off the canvas
3. A hand that slides on group of objects around or off the canvas

All great ideas.

Extend the "hand" paradigm - for example, an animated hand to "slap" items off the screen, or a hand that would grab items (like the hand that draws from behind..?), to remove items.

Removing and moving objects is a real area that could receive some attention.