Of course it would be *possible*. As the 737 is a dual pilot ship, you need two pilots who are checked out on the 737 to be able to legally fly it. As PPL, you can then sit in the RHS and fly it while the LHS is PIC and the FO is standing by just in case.
And if one of them is a type rating instructor for the 737, you could even log them as "dual" in your logbook.
Whether it's *affordable* is a totally different matter...
This all assumes a no-pax fun or training flight. If there's passengers on board, I'd say forget it. I don't think any airline would allow this anymore, unless you happen to personally know the captain or FO, in some places.