What Happens When Your Insurance Company Denies You Coverage In Florida? Can You Sue Them? Yes, you can. A lot of times, after you’ve been in an accident, your insurance company isn’t your best friend. And they may deny you coverage unlawfully for insurance coverage that you’ve paid for. When that happens, Demesmin and Dover are here for you. So call attorneys Victor Demesmin Jr. and Jeremy Dover at (866) 954-MORE (6673). We Care More.