Paintings are traditionally on stretched canvas attached to a wooden frame. Oil paintings take weeks or months to dry, so have to be stored standalone, but acrylic dries in under a day, so you can stack up finished paintings. Still, the wooden frames are bulky: it takes up as much room as the area of the painting times the depth of the frame. Storage space can be a problem.

One dodge is to have a series of frames that nest inside one another. The paintings can be stored nested like that, at the thickness of just the canvases plus one frame. It would help to have several identical series of frames like that, so that if some of the paintings are sold or given away, others can be substituted in the nesting.

Another dodge would be thin frames, metal or plastic or fiberglass, that are angled about 45 degrees from the canvas rather than 90 degrees. Then frames of the same size will nest at about a canvas width apart. Thin frames would want to warp, which could be reduced by having them cupped. Make them 1/8th of a tube, level with the canvas to start with and curving to 45 degrees from the canvas, with the canvas wrapping around the outer surface and being pinned either to the far lip or the inside surface. The canvas will pull the frame towards the center. Wider frames will resist that better. Rounded corners would be good if possible. Perhaps plastic frames, where you staple the canvas to the plastic with the staple going through the plastic.

These 1/8th-tube thin frames are something I'd expect to see in every art store, usually with prestretched treated canvas already attached. But I've never seen them. And I can't find anything that looks like them on the internet. Seems like a market opportunity being missed. They let you use real stretched canvas and store about 10x more pictures in a given amount of space.