If you are remote or have remote students, give choices and picture models for them to make up one of their own each week to keep handy at home :) Encourage use of everyday items, such as buttons, spoons, or natural or recycled materials. This is a no-cost to low-cost solution.
"Design" your boxes to go with science exploratory units, math lessons, or word-building and letter practice. Using materials already on-hand should keep you from spending more time out of your already-stressed schedule and once they are established, they'll be in a rotation and just require occasional tweaking :)
Science kits would be fun, too! Make a box of sticks. leaves and pine cones to examine, build with, sketch, etc. I threw in stripped crayons for leaf rubbings, too.
A small magnet and some metal/non-metallic items would be a great exploratory box. Add in a bunch of large paper clips for extended chains.
If you have access to craft sticks (colored ones are even more fun!) and Velcro dots, you can make a set of attachable sticks to form shapes and letters. Just put velcro on opposite sides of opposite ends and stash them in a plastic bin - fun and learning!
Pipe cleaners and beads for beading and patterning could be another box, using things you may already have access to in the classroom. Great fine-motor work!
You could try some force and motion cars and blocks, some Playdoh for many purposes ... use what you have around to make up as many mini-boxes as you want.