Yes, you can always purchase more coverage then what your state mandates you have to file the financial responsibility certificate (SR-22).

So if you have recently purchased a new car and need not only liability coverages but full coverages, meaning physical damage coverages of collision and comprehensive, then you should be able to obtain all of these coverages on your auto insurance policy.

If you cannot get both types of coverages with your current insurance provider you can click here for a car insurance quote.