My company can't use anything beyond ver.3.6 but, I want the latest version. Can I run both?
My company's website can only handle ver 3.6 and I want to run the latest version. Can I run both?
Wšykne wótegrona (1)
Yes but only one can be your default browser.
See http://kb.mozillazine.org/Using_multiple_profiles_-_Firefox
And take a backup while Firefox is down all of your profiles before hand to an external drive and store offline. It's easy once you've created and used different profiles once. You on a Mac so I can't provide details but you want to backup starting with the folder above the one your profile is in. You can find the profile you are by typing about:support into the location bar, then click on button "Open Containing Folder" that is your profile but since you will be having multiple profile go up one more director above that and backup that folder.
Whether you know what do with the backup now is not as important as having them.