You might want to visit a scale house (without a trailer) and ask. Some will, some won't. Scalemasters are the best source of info for this stuff. Take a pen and paper to make some notes with. Good Luck!

I think the clear answer comes when you specify what the gross weight of the combination will be. Just being a combination may answer the question. I'm not sure.

You will not be able to afford to do it on a part time basis. You have to do everything as the big trucks, including stopping at scales. Dually's are also targets for roadside inspections.

Three cars on a dually open & definitely enclosed will most always be over 26k, so apportioned plates IFTA etc. Insurance is also higher for auto haulers.

ANYTIME you are being paid to move freight, either cars, shingles, ect.... you are to stop at all state run scales. And also, if you plan on moving cars you will need to register for a DOT number and make sure to have your equipment licensed properly (26,000lb plates) and annual DOT inspection.

I ran hot-shot for a year back when I was 18-19 and it was bascially the same regs and rules as being in the big truck

My opinion is the same as LBZ. You will not be able to afford to run this type of operation part time. The fees and insurance will kill you. Car hauling insurance is pretty high and if you are doing enclosed cars there value will likely be more so you will need a higher amount of cargo insurance.
As far as scales you will have to stop at every one of them. Some states do go by registered weight but you will exceed all those. I think oregon is 20k but you will need to be at about 30k. I use to haul a 2 car enclosed with a dodge dually. Enclosed cars a some what seasonal so like anything else when supply goes down so do rates.
I could stay at 26k with 2 cars but barely.
Hope this info helps a little. I just dont think you could do it part time and do anything but go bankrupt. Even running full time I sometimes barely made a profit. Ofcourse this was a while ago maybe things have changes but I doubt it. Probably have gotten worse.

if you run under a dot number, yes