Multiple Versions? No.

Script Submission Tip:

If you've submitted a script to a theater, and haven't heard from them, don't send the latest version of that same script. Far better to submit a new script, and mention that you have a new draft of the previous script to send if they are interested.

If the readers aren't intrigued by your earlier draft, chances are they're not going to suddenly be swayed by the latest draft. If you're sending multiple versions, you're also sending the message that you don't know when a script is ready to be seen.

Of course, if the theater actually requests your latest draft, by all means send it. But don't confuse the invitation to "send us new work in the future" with a request for another draft. When those response letters say send us something new, they mean a completely different concept. They've seen something interesting in what you've sent the first time, and they want to see if you've got more than one script in you.