Is there a way to install a new version without removing the old? (please read)

Rather than posting to another that I’d started, because it’s related, I’ll start a new one. I have a site that’s running on Enfold, but when I upgraded the PHP in it everything crahed. The solution that I was told was to update Enfold to the newest – but I’d lost the key to the old one, so had to rebuy it. How can I move what it’s running on to the newer version, without uninstalling, then installing the new one – because the potential for errors is HUGE.
Thank you!