Some do allow open legs but in the case you mentioned you'd be better off and get better odds if you bet Team #1 straight and then after it won called back and made another bet using all the proceeds from Team #1.
The books give lower odds on parlays then straight bets so the only time to bet a parlay is when the times for 2 games overlap.
I have decided the game I want on Saturday is a game where I am guessing the line will move against me by kickoff. As for the other game, I don't know for sure what I want yet.