Managing personal Outlook.com account settings, security, and privacy
Hello DavidMcCrudden
Hi, I'm Karl and will be happy to help you today.
It's not possible to open multiple accounts within a single browser session.
What you CAN do is use a private browser session for each account - which is as close as you will get to doing what you want. (right-click on the browser icon on the task bar and click on incognito / InPrivate to lauch a new browser session. In Edge, you can also create different browser profiles for each account.