Unfortunately no. You can only remain logged into one account per provider at a time. If you need to access multiple accounts from the same provider you will need to log out of one before logging into the second. This is due to restrictions within the account authentication.
You can however stay logged in to multiple accounts if they each have different providers. For instance, you can connect and remain logged in to 1 Gmail account, 1 Yahoo account and 1 Outlook account all at the same time.
We regret any inconvenience this may cause.