Every trip I've done has always required a one night stay, though not always a Saturday. The one I'm on right now (I'm at Dulles between flights) allowed any day of the week for the one night stay. This is usually not the norm, though, as most sales require a Saturday night stay.

I think what others are suggesting is called "nesting", where you combine several trips into one. I tend not to do that so can't comment on it directly.