If you want to get maximum compensation and all insurance coverage has been exhausted, then you could file a lawsuit to obtain an excess verdict against the driver at-fault. However, local civil courts are quickly overwhelmed by endless car accident lawsuits due to the high prevalence of auto accidents. Getting the maximum compensation possible for your claim in such a burdened system requires a lawyer's experience and knowledge.
The difficulty of obtaining the maximum compensation depends on various criteria, unique for every case, such as:
Considering all these factors, you need to be aware that the compensation you require and the one the court will agree on can differ significantly.