With most SS sets, the large lid is designed to fit the stock pot and the frying pan. When looking on line, make sure you look at the specifications and take careful note of the width of the frying pan, cover and stock pot. I would rather buy and shop for in person, individual pots than a set. It might be more costly than buying a set, but you would have exactly what you want and need. And think of all the fun you will have seeing and touching all those beautiful pans.
I would think if the cover fits too tightly on any pan, you are almost creating a pressure pot atmosphere inside the pan. That could be come dangerous.