So, you want to write a screenplay with multiple stories. It definitely can be done and done well. Take the 2006 Best Picture Academy Award winner Crash as an example. However, writing multiple storylines is no easy task, so it's best to stay simple, especially for the beginning writer. Even Crash – with its interweaving stories – is simple in structure. The story is told in chronological order with inter-related characters over a period of over only two days. Writer/Director Paul Haggis doesn't try to cover too many events, too much time, use non-related characters, or non-linear order. For Haggis' Crash, the old cliché holds truth: less is more.
Whenever a screenwriter in one of my writing workshops asks about approaching a script with multiple stories, I first advice him or her to kill some babies – pick the very best story and stick with that. However, if the writer persists – and he or she may be right to do so – I reiterate the importance of simplicity. Less really is more. A screenwriter's job is not to reinvent the wheel. The wheel works perfectly fine already. Great screenwriting is based "less" on complexities of plot and "more" on interesting characters in a memorable world.
So if you're heart is set on writing a script with multiple stories, make sure you have kick ass characters in a kick ass world, and then... do a lot of research to help you with structure. Watch as many movies with multiple storylines as possible. Don't worry about genre; just focus on how the stories are told.
Besides Crash, here are a few films to get you started: Love Actually, Adaptation, and Vanilla Sky. Those films all have multiple story lines, with the main tension of each story directly connected to what is going on within the current world. If your story takes place over a longer period of time, however, The Fountain and The Red Violin are two films to check out. In The Fountain, three story lines interconnect yet remain separate, isolated by their different time periods. In The Red Violin, the violin itself is the object that connects multiple stories over a period of centuries.
Remember, one of the best ways to learn to become a better screenwriter is to watch a lot of movies and read a ton of scripts. So get your Netflix streaming and the popcorn popping, and with pen and paper in hand, watch and learn.