Yes. There are other parties in addition to the at-fault driver who you can sue following a motor vehicle accident in Florida. These are the owner of the vehicle driven by the at-fault driver. In addition, you could also sue your own insurance company under your uninsured motorist protection. Uninsured motorist protection is purchased in the event that the at-fault driver and other parties do not have sufficient insurance to cover you for your injuries in a motor vehicle accident in Florida.