Most recently, Messenger updated to add new features like Android, supporting you to log into multiple accounts on one app.
First you can go to the Appstore of the device's app store to perform the update.
Go to "Appstore" to check for updates
Next immediately update "Messenger".
Updated mesenger
After updating you go to settings "Me".
Choose me
To add another account you choose to go to "Transfer account".
Account transfer
You will select the "+" symbol.
Select the + sign
Login to your new "Facebook" account.
Sign in with your new Facebook account
You can only "Online" on one account at the same time, to re-sign the logged-out account, you just need to "Touch" on that account.
Tap on the account to re-login
Select "OK" to agree to login.
Select OK to agree to login
In addition, you can also delete certain accounts that you do not need to use by swiping the account from right to left.
Select "Delete" the account
Good luck.