Yes, you should be able to obtain full coverage as well as the required SR-22, which usually is at least the state required liability insurance.

You should be able to talk to your insurance agent about carrying the required insurance for the SR-22 plus the physical damages coverages that would be required by the lien holder of your financed car. You should be able to obtain both types of coverages to maintain what the state and lien holder will require of you.

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