Several years ago I decided to fly from SFO to a convention in DC by way of Berlin. The cheap (winter) Berlin fare didn't allow any stopovers, though, and 24 hours wouldn't have done it. So here's my solution:

I bought a round-trip to Berlin, with a plane change in DC on the return. My company bought a ticket SFO to DC & back, with the return at the end of the converence. Then I sold the company's outbound plus my ongoing coupon to a fellow at the gym.

That was back before they checked IDs on domestic flights, but it could still work, albeit illicitly. Make the 2nd outbound leave at a time you can accompany your friend to the airport and check in for him. And you'll be trading tickets at the stopover airport in any event, so that leg you've already checked in and he just takes your boarding pass and gets on board.

The fellow I sold these to (a stranger) was leery, since he'd be in DC without "his" return ticket...but then he realized I couldn't leave DC without hooking up with him, so figured he was OK! And it went off without a hitch. I even offered him an upgrade (at his expense, buying coupons) either direction.