Getting back to the orignal question...
Years ago (almost 30), I flew the 727 (both the 100 and 200), and it, in fact, could fly on only one engine. But, you had to have speed, no drag, and you had to realize that you were limited in terms of density altitude.
If I recall (others, help me out, please), you needed to be clean and have 200 KIAS. Then, you would be able to fly.
For example, coming down the glide path with only one engine turning...limited flaps/gear down...and, you decide to go around (for whatever reason)...you had to get the gear and flaps/slats up, and accelerate to about 200 KIAS (as you continue down the glide path). Once you got clean and 200 KIAS, you would be able to climb.
As memory serves, based on typical gross weights, you were limited to maybe 6000 to 8000 feet density altitude. But, at least it would fly.
I don't have any experience with any other three-engine aircraft, so I can't speak for the TriStar, etc. However, I DO remember that flying the 727 with only one turning was a required maneuver in the simulator to obtain the type rating.
Fly safe,
PantLoad