Each version needs to be placed in its own Programs Folder. Also, each must have and use its own profile.

What versions is this about ?

Installing multiple versions on Mac OS X is basically dragging the Firefox application out of the DMG file to the desktop and rename the folder.
You can drag the renamed Firefox application folder to the Applications folder like you would normally install Firefox.
You can possibly eject the DMG file and and trash the installer.

You may need to use the terminal to create a new profile for that version.

• https://support.mozilla.org/en-US/kb/profile-manager-create-remove-switch-firefox-profiles
• https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile

Firefox 67 and later use a dedicated profile for each installation folder and lock this profile to prevent other Firefox versions from using this profile.

• https://support.mozilla.org/en-US/kb/dedicated-profiles-firefox-installation

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What extensions are working in Firefox 68 ESR (note that current is 68.11.0) and not in Firefox 78/79 versions ?

This would only happen if an extension uses an API that is no longer supported and that hasn't been updated by its creator (i.e. it is abandoned).

I don't use Firefox ESR version

With the 68 ESR version at least you have a Firefox version that is still supported with security updates (68.0.2 => August 14, 2019).

• https://www.mozilla.org/en-US/firefox/68.0.2/releasenotes/

Can you tell us which extensions are holding you from using the current release as there might be alternatives ?

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