To connect multiple Twitter accounts to Groove, go into your Apps > Twitter > Settings. You will see a button at the top of the window to "Add a Twitter Account".
Next you will be prompted to authorize Groove from your Twitter account.
Please note that if you are already logged into a Twitter account, it will attempt to authorize that account. To authorize a different account you will need to log out first.
You have the option to send your different Twitter accounts to your different mailboxes by selecting the mailbox from the dropdown menu on the right.