I do not think you are able to fly on other airlines. I believe you have to fly on delta planes (or delta connection carriers). Once, AeroMexico and Air France were eligible, but no longer. Just because a flight shows up as a Delta flight on the main Delta customer website does not mean it is a real Delta flight — It could be a codeshare flight that pass riders wouldn't be eligible for. You should be able to find a Delta flight to most anywhere that you want to go, or close to it…Where are you trying to go?