How to create and log into different organizations with one account?

Thank you StevenC365! Just to be clear though, those other organizations I want to be part of should still be under my control. So I don't just want to be a guest in my client companies' orgs, I want to create my own orgs, e.g. one for all the people I work with at company A, one for all the people I work with at company B, and so on. Does that make sense? In the screenshot from my personal account, you can see that out of the five orgs, I'm only a guest in two of them, the other three are my own. That's what I would like to have.

And the problem is, I can't seem to be able to invite myself into orgs that I created in Azure. If I go to Org2 in Azure and try to invite my primary handle (...@org1.onmicrosoft.com) as an external user, I get the error that this username already exists in this directory, even thought the list of users only shows my secondary handle (...#EXT#@org2.onmicrosoft.com) with which I can't log in or do anything else.