You need to be clear (with your own self) why you have a segmented screenplay.
Stories that become one
This is the most obvious, but also the most complex. At some point the various narratives will need foreshadowing and unforced plot alignment in order to not break your contract with your audience. Keeping track of each individual segment's storyline and character dispositions will be very difficult if you write each separately - by the time you write the final segment, it will be constrained by the other two. Clearly, writing the three stories in tandem would work best here, as each will draw on the growth of each other and be more fluid and cohesive as a result.
Stories that remain separate, but share a theme
This is less complex than merging stories over time, but will require your theme to be fully understood before you begin. If you develop your theme over time, each successive segment will have more depth and may leave the audience somewhat unfulfilled since the end result will jump between stories and the strength of the theme will come and go. You could make this work for you, but it will be extremely difficult to get right. In Stephen King's On Writing, he firmly points out theme as an element to be aware of, but only to focus on in final edits. I agree: theme driving story equals morality play. Assuming your theme exists and is clear, and you will return to fully flesh it out in later edits, then writing each story separately makes sense.
Stories that are separate
This is the easiest to write, but will be the most difficult to cut up. You run the risk of slicing in ways that will have unintentional consequences for the audience, and often you will not pick this up given your close involvement. The amount of rewrites may become more effort than the project is worth. And the question has to be asked: if the stories are separate, and there is no uniting element (plot, theme or shared characters), then why have them together at all?
Story telling can be just for the author, but I firmly believe that a story isn't worth much if it doesn't have an audience. And audiences (with the possible exception of genres like mystery, I guess) don't want to be confused. Your contract with them is to entertain, to make them think, to help them suspend disbelief and enter another world. If you disrupt their engagement, you may not get their attention back.