Kind of I think they need a book called "CDL laws for dummies" lolTechnically yes. However, the only way to have a Class A is 1. have a K restriction which restricts your CDL to your home State or 2. have a medical card. If you have a K on your license, then it would be up to the current State you are in if they want to honor your A for a private vehicle. Also, if your Stated requires a Class A or B for the vehicle you are driving or a special endorsement then you would be operating out of Class depending again on the State you are currently in. Clear as mud?