You could get a clear plastic shallow bin with relevant dimensions to fit on a shelf in your fridge. Then you can take it out and put it back as needed. I just use the vegetable drawer in my fridge though.

The vegetable box on mine makes things last a long time with a filter for ethylene gas, perhaps something like these could help: https://www.amazon.com/ethylene-gas-absorber-fridge/

OXO Good Grips GreenSaver Produce Keeper is a pretty good lil product.