TravelBuzz or a particular airline is probably a better place for this post. MR'ers want to minimize the cost and finish the trip asap, they are not looking for an overnight so its really not applicable for them. (PM a moderator from this forum, they'd be glad to move it for you)

As far as your question, you'd have to book the first flight leg to arrive after the last connecting flight to your destiniation has left, then book the first flight out the next morning to your destination to accomplish the nights stay without being considered a stop. Enjoy.