All the advice here is really good, but I have something to add. In my opinion, the best way to easily differentiate all of your multiple plotlines is to have each one be related to a character. I'll use my own fic as an example. I try to avoid specific examples, but it would get confusing if I didn't use names. Here are my plotlines:
The Keith Plotline - named after the main character, this one involves Keith traveling Kanto to better himself and answer his many questions (eg: training under Sabrina, looking into what Pokemon attacked him at Cerulean Cave)
The Criss Plotline - named for a vigilante character that fights Team Rocket, this one involves just that, fighting Team Rocket (although there is a little more to it than that).
The Nolan Plotline - This one's a little different, as it's told from the PoV of Nolan rather than Keith. It involves discovering who Nolan is, Criss's past, and some fighting of Team Rocket.
The Tim Plotline - named after the main character's best friend, this is the generic journey fic plot. Go from gym to gym collecting badges until you can fight the Elite Four.
Whenever I want to switch between plotlines, I just change which character the focus is on. If Keith's alone and introspective, it's the Keith plotline. If Criss approaches him with a plan on attacking a Team Rocket base, etc, it's the Criss Plotline. If it's told from the PoV of Nolan, it's the Nolan plotline. And if Tim is getting all excited about battling, or Keith and Tim are just hanging out, battling, or talking, it's the Tim plotline. Everything stays separate because, for example, Keith doesn't know who Nolan is and Criss doesn't really care about the gym challenge.
Hopefully these examples aren't too specific and you get what I mean. Just have each plotline be driven by a specific character. It helps keep things from getting entangled.