OK, I had the opposite experience. I was booking a round trip from home port to LAX leaving Sunday.
Now, my home airport was notorious for very high fares, such that we often shopped around for other fields within driving distance (there are several).
So, I made it known that I would be staying overnight the preceding Saturday in another city, and perhaps the agent should explore that opportunity. Agent thought a minute, said "You're staying Sat. night, right?"
"Yes"
"I'll call you right back" - which he did. "Here's what we'll do. We'll fly you to your Sat. location, buy the room, taxi, and meals, fly you back to home city to catch the LAX flight, then fly back home at the end of the week. And all this saves your company $400 or so compared to standard RT fare"!
Oy Vey!