Yes, it is possible to add a vehicle to your car insurance policy that is not titled in your name with some, not all, auto insurance companies.
State laws govern auto insurance so they would need to allow this type of policy in your state and then it would be up to the individual insurance companies' guidelines from there if they will permit you to insure a car titled in someone else's name.
Normally you need to be the owner of the car and have insurable interest in it to place car insurance on a vehicle. Having insurable interest in a vehicle basically means being an owner of the vehicle, co-signer or lien holder.
Most automobile insurance companies will not allow you to insure someone else's vehicle, because you do not have insurable interest which means in the eyes of the insurance industry you would not suffer an economic loss if the vehicle was damaged. The ones that would suffer an economic loss (owners, lien holders and co-signers) are usually the only individuals permitted to insure vehicles.
Most CarInsurance.com companies require that your name appear on the title or registration in order to be able to purchase an auto insurance policy in your name for that vehicle. There are however, insurance companies that will allow you to obtain insurance though you do not have insurable interest in a car if you have care, custody and control of the vehicle. Esurance is one such company.
We do work with Esurance and in certain states they do allow policyholders to add a vehicle to their policy though they are not on the title of the car. If you obtain such a policy with Esurance, they will require that the owner of the car be listed on the policy.
If you already have a car insurance policy in place that you wish to add a car to which you are not an owner of, it will depend upon your state insurance laws and your car insurance company's guidelines if this is possible or not. Contact your current auto insurance provider to ask if they will permit you to insure a car that is titled to someone else.
You may find you will need to shop around for car insurance to fit your situation. You can get started here with instant car insurance quotes. If Esurance is a choice that comes up then finish your quote with them to see if in your state they offer the coverage you need on the car you do not have insurable interest in. If you need help with the quote you can contact CarInsurance.com agents at 1-855-430-7753.