I have done this on UA's international awards using a little known feature called a "forced stopover".

So when I flew from xxx-HKG, I flew late enough into SFO to miss the daily SFO-HKG departure by one hour. This left 23 hours in SFO until the next UA flight to HKG.

On the way back, I had 3 days scheduled in SFO. This was my ACTUAL stopover.

UA allows EITHER one stopover or one open jaw. But you can actually add a "free" forced stopover.

Note that the hotel, transit, nd meal costs on the forced stopover must be covered by the pax.