Flat towing with a 3rd row?

Personally, I do not know of any 8 to 9 passenger vehicles that meet your specifications. AFAIK, "big SUVs" are the only ones. In order to be towable, it will likely have to be four wheel drive, with a NEUTRAL position on the transfer case shift. It is, however, possible a lube pump can be installed to lube/cool the transmission ($1000, more or less). Such a rig will be fairly heavy, quite possibly in excess of 5000 lbs(especially if a lot of "stuff" is carried in it).
Motorhomes normally have a towing capacity of 3500, 5000, or 10,000 lbs. The 10K towing capacity is, in my experience, usually only found in high end diesel pusher coaches.
Good luck in your search.

Ford Flex is what we tow. But it is not a mid size vehicle..

Chevy Traverse, Buick Enclave, GMC Acadia I believe all have third row seating options. Don't know about towability of current models.

We have a Ford Freestyle (now the Taurus) with 3rd row seating for a total of 7. Volvo XC also has 3rd row seating as well as those mentioned already.

Ford Explorer.

Jeep Commander and the current generation Dodge Durango (both based on the Grand Cherokee) have third row options and should be flat towable in 4WD trim, if they have the low range transfer case with neutral. There were AWD options without low range that are not flat towable, so you need to check and make sure it has a neutral position.