Office 365 + Outlook 2016/2019 + Windows 10 déconnectés

I haven't seen issues with multiple accounts in Outlook for years now, and I use several in my day-to-day tasks. So the first thing I'd advise you to do is to make sure you are running an updated version of Office, switch to the Current channel if necessary. Running the SaRA tool might help detect some misconfigurations: https://diagnostics.outlook.com/