This is probably entirely unhelpful, but...
1. Have a starting point.
2. Have an end goal.
3. Just write.
Essentially, let new subplots develop as you wrap up the old ones. For me, I just trust it'll fall together and in almost all cases it does. It's much harder to do that writing a novel or book. Something about a TA makes it easier to develop without having a definitive script.
1. Started with nerdy science teacher on a routine "mission" in the desert.
2. Mission gets derailed and now I must get to the rendezvous.
3. All my puzzles were subplots.
1. Wake up in prison. Must escape to safety, hoping to learn stuff about what you got into along the way.
2. Find out who bad guy is and escape to nearby village.
3. Write subplots.
X3 (just started):
1. Wake up in village.
2. Final confrontation with bad guy.
3. Writing subplots.
Maybe that works for only "wingers" like me? Maybe you've tried that and it doesn't work for you? Personally, I really enjoy opening it up and discovering where the story leads. To me, that is the most fun part of writing TAs. It's almost as if the story is telling me a story.
Perhaps this turns my plots into chaotic garbage but in my honest, biased, opinion I think they're great!