Where can you get new insurance regardless of the rate when your company refuses to renew your policy due to 2 minor accidents in the last 3 years?

InsureMe is a good option. Some states have "assigned risk" policies. In order to receive a license to sell insurance in these states, a company has to agree to accept a certain number of high risk drivers. The agent from the cancelling company should be able to tell you if this applies to your state and where to get an application if it does.