Using apps from different plans on the same user login?

Hello!

I have a small problem I can't figure out. I have had a personal plan for some time where I have Photoshop and a few other apps. Recently I started a company and made a company plan where I bought Indesign, which I will use for my company. I keep it like for bookkeeping reasons. But since I am the same person I figured I could invite my private user to use the Indesign license.

But what I find now is that to access Indesign I have to log in to the "business account" and then Photoshop becomes unavailable since it is on my private plan, I have to log out and log back into my private account. This seems inefficient, is there no way I can remain logged into my private account since my business invited me to that license?