Can you insure a car that is not mime and has no other insurance policy on it?

You cannot insure a vehicle that is not yours. Whether or not it has current insurance on it does not matter but the fact that it is not titled to you does make a serious difference. An insurance application together with the policy make up a legal and binding contract and it states in the policy that you must own the vehicle or have an insurable interest. In a situation where you lease the vehicle does give you insurable interest and allows you to insure a leased vehicle even though it is titled to the name of the bank or finance company who leases it to you. In one example where a problem would arise lets say that you have physical damage coverage on a policy and it a tree thereby causing a total loss to the vehicle. The insurance company cannot legally pay you for the vehicle because it is not titled to you and they cannot pay the bank or finance company because they do not have an insurance contract with then to insure the vehicle. This is just one example.