Yes, unless your "middle" trip is back to your originating city AND your original fare required a Saturday night stay AND the "middle" trip eats up all the Saturday night stays from the original trip.

If you just want to go somewhere else, you're OK. I've done this myself.

I've even done a trip where I've connected through my original city. I've never done a stopover in my original city, though. That might be a marginal case.