There's no way to do that with the default Like box. What you could do though is create a custom Like button using our Open Graph Actions integration. The action type is built-in to Facebook and called 'og.likes'. We have a
Open Graph Actions configuration guide
that could help with that.
You wouldn't need to create anything in your Facebook Application, so just skip to the Action/Object creation in Joomla. You can use the og.likes on any type of Object, so create your objects however you want. Then add the {JFBCAction id=xx text=I like this} tag wherever you want the button to display.
The main reason this may be beneficial is that you can set the Explicitly Shared option in the action (both in your Facebook App and the Action in JFBConnect). With that, Facebook should give the action a lot more weight and (from what they say) it should be shown prominently in their Timeline.
I hope that gives you an idea to investigate, but if you have any comments or feedback, let me know.
Thanks,
Alex