Yes, you can. It's pretty common between family members: husband/wife, parents/children, etc. Taking it off one permit to put in on another is only necessary when you sell the gun to someone and no longer own it. When it is between family members, you still own it but the other person is authorized to carry it.
In my NRA class, they strongly recommended doing that if your household has more than one permit holder: put everybody's guns on everybody's permit. They cited a case where a man was taken to the hospital after a car accident, and his wife (who was also in the car but wasn't hurt) wanted to take possession of the handgun that he had on him at the time of the accident. She had her own permit, but his gun wasn't listed on her permit, so the cops wouldn't let her take it. They confiscated it instead, and he had to reclaim it when he got out of the hospital.
Last edited by toivo; 05-26-2009 at 02:04 AM. Reason: spelling
They call it "co-own" in Dutchess. You have to either both go to the Pistol Permit office and sign the forms, or bring a letter from your spouse agreeing to "co-ownership" of the gun in order to put it on your permit. The accident/hospital scenario is quite accurate, and also in the unfortunate event that there is a death - this allows the spouse or other co-owner to take the gun collection hassle free.