Yes. If you're on android or iOS the game refers to your browser (or possibly the FB app, but I uninstalled that so it looks to my browser) to get your Facebook info.
So if you want to create a new TSB team and register it to a new FB account:
1) log out of baseball team in the app. 2) log out of your FB profile in the FB app and/or browser. 3) log into your new FB profile in FB app or in your web browser. 4) load up TSB and click Login With FB.
This should guide you to registering your new team to the new FB account. If it logs you back into your first team, try repeating the steps but completely close the TSB app after step 1.
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So if you want to create a new TSB team and register it to a new FB account:
1) log out of baseball team in the app.
2) log out of your FB profile in the FB app and/or browser.
3) log into your new FB profile in FB app or in your web browser.
4) load up TSB and click Login With FB.
This should guide you to registering your new team to the new FB account. If it logs you back into your first team, try repeating the steps but completely close the TSB app after step 1.