I almost never have more than two pots cooking at the same time, and they are either 8 or 10" diameters, as are most of my pots. The dish drainer is as close as these ever get to being put away, since they are used so much. I put the other lids in deep storage. I chose glass ones, since they are easier for monitoring the contents. I also have a 12" lid that I can get to readily, for the less frequent occasions when I use a larger pan. You can buy a multi-purpose lid that will work on various diameter pans.
https://www.amazon.com/RSVP-Endurance-Stainless-Universal-Insert/dp/B0017U1Q4G/ref=sr_1_1?s=kitchen&ie=UTF8&qid=1472417655&sr=1-1&keywords=multi+pan+lid
https://www.amazon.com/Tops-Mfg-55709-Fitz-All-Cover/dp/B000HM9Z9I/ref=sr_1_3?s=kitchen&ie=UTF8&qid=1472417728&sr=1-3&keywords=multi+pan+lid
Never thought of this, but good suggestion. I’ll think about this when I start losing or breaking all my lids. 
