If your son is getting the Mustang registered in his name, he should consider getting his own policy on the vehicle. Without the vehicle being in his name it might be difficult for him to get a separate New York auto insurance policy.
Many companies have an option called umbrella coverage. Insurance providers offer umbrella coverage so you can increase your protection beyond the limits of your policy. So yes, companies do offer blanket policies or personal liability through the means of an umbrella policy which gives coverage for liability.
For an umbrella policy you list what items you want covered (i.e. home, boat, cars, motorcycle, etc) and then those listed items are underwritten and a rate is given for the premium to cover up to $1 million in liability.
Some companies only offer umbrella policies if you insure both your home and car with them. We have partnered with Safeco to help you find the best rate for Umbrella insurance.
Safeco's Personal Umbrella policies are competitively priced and offer exceptional coverage. You can receive coverage up to $2 million. Umbrella policies are available to Safeco customers who insure their personal autos with Safeco. You may have to have certain liability limits in order to qualify for Umbrella insurance (availability is subject to state laws, compliance and underwriting).
As for the drug or alcohol issue, these items do not typically void a policy but you should read through your policy or speak with your insurance agent to find out if it is a listed exclusion for you particular coverage.
See our article The Basics of a Personal Liability Umbrella Policy for more information on this subject.