Yes. You can switch insurance companies at any point, even if you have an open claim with your old company. As long as you make the claim before the switch goes into effect, your old insurer is obligated to follow through.
Policyholders occasionally switch companies if their current insurer is stalling the claims process. If you feel that your insurance company is mistreating you, it is your right to obtain quotes from other companies, though specific laws and procedures vary by state.