Two Adobe accounts, one computer, without logging in and out of CC repeatedly

I work for a university that has an institution-wide enterprise license for Adobe Acrobat. Through my department, I also have a Creative Cloud Photography license. For the past few years, I've used both side-by-side without having to log in and out of my Adobe accounts constantly.

Similarly, on my home computer, which I've been using for work the past couple years, I am able to use Acrobat on my University's enterprise license while simultaneously using Photoshop and Lightroom on my Adobe CC Photography license without logging in and out all the time.

However, I had to get a new computer for work and now, in order to switch from Photoshop to Acrobat, I'm forced to log out of one Adobe account and log into the other. This is a massive waste of time and is viciously tedious. I've talked with three people at Adobe and my University's IT department. All of them  have this "Can't get there from here" attitude, and nobody can tell me why, on two separate machines I can do what they say is impossible.

The experts have failed, so I'm consulting the crowd. What is going on here? I know it is possible to use my institution's enterprise license of Acrobat at the same time I'm using my own or my department's CC Photography license, but I can't figure out why it only works on 2/3 computers. The OS and software versions are all up-to-date, incidentally.