In the next few weeks, I have two 3-night trips. So, I'm checking out of my first hotel after one night, then checking into another, then another (or even back to the original). Counts as three stays in each trip.
Ah, the things I go through in order to accrue points. If I were to look at the dollar value, it's almost certainly not worth all this effort. But business travel gets pretty old sometimes and playing these games livens things up a bit.