Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
Hi Daniel,
Thank you for posting your query on Microsoft Community forum. When you say "I have my own personal account and a separate (my employer's) account", may I double confirm whether both are Office 365 Business Exchange Online accounts or one is personal (e.g. Outlook.com) and another one employer's Business Exchange online account?
Do you want to download/install both Office 365 Personal and Office 365 Business desktop client app (such as Word/Excel etc.)? If so, it's not feasible to install/use both subscription on the same device.
However, if you want to access emails from both the accounts using one device. You may use two different browsers such as (latest Edge/Chrome/Firefox) to sign into Outlook Web App with different Office 365 accounts.
Moreover, if you have latest Outlook 365 desktop client you can add/setup both the accounts on profile, it will be separately. For your reference: Add an email account to Outlook
If this is not your requirement or I have misunderstood anything, please correct me and provide us with detailed information including example about the requirement via the private message so that we can check to further assist you.
Your patience and cooperation are highly appreciated. Have a nice day and stay safe!
Best regards,
Shyamal