I play catcher for a very informal "beer-league" softball team, and have realized that I prefer different gloves at different points in the inning.
With no one on base, I want a big outfielder type glove for catching foul-tips and short pop-flys. A catcher's glove isn't as reliable for a novice player like me.
Once a runner is in scoring position, I want more of a traditional catchers glove, because it has a lot of catching-and-trapping power, so I can reliably catch balls thrown full force from the outfield to home-plate ahead of the runner.
I haven't asked the umpires yet, but would it be legal to keep a second glove near the backstop, and switch gloves once a runner gets to 3rd?
What about in more professional leagues? Could players change gloves mid-inning? (provided it does not delay the game) Are there good reasons to do so?