No - Not unless you want to or your computer resources are compromised by having programs that you do not need on the computer.
Adobe typically has that message that you do not have to uninstall older to install newer. Just use one at a time.
Adobe allows you to have the same purchased activated serial number on no more of 2 of your computers. And, you are supposed to run one at a time.
But you do not seem to be asking that question. You seem to asking if it is OK to leave older versions on the computer as you move on to the new version.
But, I would suggest that you keep the oldest working version on the computer until you are sure that the new version is working.
Please review and consider. Any questions, please do not hesitate to ask.
Thanks so much!!