Hi Michael,
The purpose of Office 365 Outlook Web App (OWA), is to access a user's primary mailbox on the browser. It is not feasible to add another account and display a separate folder, as shown in the Outlook client.
If you are connecting a Non-office 365 account in Outlook on the web which is outside your organization, then you can only add the connected accounts, in which the emails can be sent and read in one place (primary mailbox) in OWA.
As a workaround, you can add a mailbox which is inside your organization. Access another person’s mailbox in Outlook/OWA (delegation), and his/her mailbox will display a separate folder on the mail list in OWA. Remember you need to change the permission of that person's folder (delegation) to access the mailbox.
We suggest you submit feedback to the related team via the link: https://outlook.uservoice.com/forums/313228--outlook-on-the-web-office-365. Many features have been designed or upgraded by customers' valuable advice.
Thank you for your understanding.
Best Regards,
Ruel
