It can be advantageous to submit several scripts to competitions as once, particularly if you get a discount with several submissions. Why not? If you have two or three strong submissions and think the more, the merrier, then go ahead.
With one BIG caveat.
If you submit three scripts at the same time, in all likelihood, those scripts will be bundled and distributed to the same reader. It’s logical to assume if Reader A read Script 1 and didn’t like it, that reader is not going to be enthusiastic about reading Script 2 by that same writer. It is possible, but you’re then rolling that boulder uphill – and why not simply start with a clean slate?
If you submit three screenplays and get assigned three separate readers, you have a better chance that your scripts will all be read with a fresh and unbiased eye.
I would actually submit scripts at different times, perhaps a couple of weeks apart, and not take the discount. Why? Because if you submit your scripts at the same time, you will likely be assigned the same reader. In some cases it might be possible to submit at the same time and request different readers. If you do go ahead and submit at the same time, it would behoove you to request separate readers. This is probably something that can easily be addressed with the contest coordinator before submitting.
Last season, there were several instances wherein writers submitted multiple screenplays, and they didn’t bother to submit the script without their name, so in reading, I knew that the screenplays were written by the same author before hitting page 1. If I thought the first submission was sloppy, trite or novice, it would influence the attention with which I would approach the next screenplay. Of course, I would still read the next project, but if I already knew that the reader was weak with character development, or plotting, then I would be more critical approaching the second script.
Every script deserves a fair shot – so be conscious about how you submit and who might be reading your scripts.