Not in FitNesse itself, but you can build it into your fixtures.
When I had a similar problem I was able to solve it using what we called "fail fast" mode. This was a static variable that could be set to true under certain conditions (typically by an element not found exception or similar).
Our main driver was structured such that we could pass through one spot that could check for that value before calling the browserDriver. This would then skip the broswerDriver calls until the test ended.
The next text would clear the flag and start up again.
You would need to manage the whole process, but it can work.