Can your step daughters boyfriend insure your car even though he is not the registered keeper or owner of the vehicle?

No. You cannot insure any car that you do not own. The only exception to this is a legally married couple who are both listed as drivers. In a married situation like this vehicles may be owned by one or another and insured on a policy together. I always list both the husband and wife as insureds on the policy so that either one can make changes on the policy and sign documents. Remember an insurance application and policy make up a legal contract.