Shared Computer Activation for Office in Microsoft 365 Business

Here's my issue and why this policy either needs to be expanded to all Business level O365 user licenses or authentication for different license levels need to be able to coexist on the same computer.

We have two room based meeting computers where it's attached to a large screen on the wall.  Right now as it stands, E3 licenses users and Business premium users can't both authenticate and use the same installed Word or Excel.  Our staff are well within their 5 device licensed limit so it should be no problem to have them authenticate with these two room computers.  But they can't.  Why?  Because if you install either of the Business premium package or the E3 package the other licensed group can't authenticate.  One would think you could install the Business Premium package and E3 should be able to authenticate since Business premium is a subset of E3.  There is nothing Business premium has that E3 doesn't also have.  But this doesn't work either.  How can I get my legally under the limit licensed E3 and Business Premium users to use Word, Excel, Powerpoint and Outlook on the same computer?  This should be a trivial thing to allow and it would be such a huge convenience especially for companies that have multiple shifts of workers sharing the same computer, but they might have different license levels.  If this can somehow be done and someone has done it, please let me know the secret.