triple towing is legal in AZ but! i am not sure if one has to be a 5th wheel set up or not and i am sure there are restrictions on total length. you may need a commercial vehicle, may need a endorsement to pull. ya may want to do a google search.
Ball to ball towing in not legal with AZ plates. You can tow a trailer behind a fifth wheel trailer. I did it for several years going to the sand dunes and never had any problems, even in California.
If you call DPS, you can get an answer to suit your needs and then run with it. My truck, fifth wheel and second trailer were 71' long. I called DPS and they told me that as long as the tow vehicle and the main trailer were not over 65' long, I could put any trailer behing that I wanted to. I know that it isn't correct but that Iswhat I wanted to hear hear so I headed out with it.
That has been almost 15 years ago so I might be off on those numbers but I know that I was over the legal limit for that era.
DPS also told me that you don't need any special drivers license, just a normal operator's license.