Are there parties other than the at-fault driver against whom I can take legal action in a Florida auto accident case?

In many cases there are. For example, the at-fault driver may be working for a construction company, and that, he's on the job in the course and scope of his employment, and you can file a claim against his employer and the employer's workers' comp carrier to obtain compensation for the damages that had been caused.

Also, in many cases, you have a situation where there's a faulty traffic light or the road has been improperly designed, and you can file a claim against the parties that have contributed to that accident to cause the damages to you. So there's a variety of avenues that you have. And you're not just limited to the at-fault driver.