Hello dean03032,
Welcome to Microsoft Community, we are glad to assist you here.
According to the error "This account is not supported in Outlook for Windows due to the license provided by your work or school", it seems this account does not have proper license or your organization IT admins has restricted the use of multiple account in Outlook for Windows due to licensing restrictions. Thus, do you have any chance to check the license assignment on this account? You can refer to What Microsoft 365 business product or license do I have? - Microsoft Support | What Microsoft 365 subscription do I have? - Microsoft 365 admin | Microsoft Learn
Typically, when you switch from Windows mail app to the New Outlook for Windows, the new Outlook for Windows will launch into the first account on your list in Windows Mail, you can refer to Getting started with the new Outlook for Windows - Microsoft Support. However, if you don't have a Microsoft 365 office apps license or if your IT admin set restriction not to add multiple accounts in Outlook, as a work around you can install Outlook PWA(Progressive Web App), after you install the web version of Outlook as a progressive web app, you can do things like pin and launch the web version of Outlook from your computer's home screen or taskbar, and access your account while you're offline. Therefore, you can install two PWAs for two accounts and pin them to your taskbar. This way, you can access both of your accounts at the same time without having to log in and out. You can refer to Use the web version of Outlook like a desktop app - Microsoft Support
Hope this is helpful, and please feel free to get back to us if you have further concerns,
Regards,
Microsoft Community