without fixing it permanently together?
This is the real challenge here as the ideal conventional fix for many loose joints forms part of the final assembly process where the pieces are being glued together. One fix that is a separate operation, glueing on thin slips of wood to fatten fingers/tenons/dovetails may be too fiddly to be practical in material this thin — I'm visualising the fingers in 1/8" ply as being numerous and small. Plus you need a hand plane and source wood to make the packing material yourself since commercial veneers are almost certain to be too thick.
So, since you've clarified in the Comments that the items don't need to be disassembled often and thinking outside the box, I think a possible solution would be to use hot-melt glue. Hot-melt glue sticks wood together surprisingly strongly but yet is easily reversible using heat of course, and even if not fully meltable at low temps a hairdryer will usually prove sufficient to get it to weaken its hold.
In addition hot-melt glue can easily be dispensed in various ways to tack adjacent surfaces together, in a manner akin to welding. This isn't normally how conventional woodwork would be fixed* and in this glue the joint formed wouldn't be particularly strong, but it might be sufficient for the type of things you're building. So you could for example assemble anything with finger-jointed corners and then apply dots of glue, or a continuous bead, along the inside corner. Lap joints could be glued conventionally, then heated through with an iron when they need to come apart.
Another option might be to actually glue the joints the normal way, but using a reversible adhesive. Hide glue (the OG hot glue although room-temperature versions can be made or bought) is probably perfect for this since with heat and moisture joints can be separated at any point in the future. But the moist heat needed does pose a risk of warping the thin ply.
*Although something like this is done in epoxy.