Extended range guitar
An extended range guitar is one with more than 6 strings. For microtonal instruments, e.g. the Kite guitar, this may not actually increase the range.
https://www.sevenstring.org/ has a lot of information, including a forum.
Sources for 7- and 8-string guitars:
Low-end (US$200-500)
Grote (China)
7-string archtop semi-acoustic
Very favorable review that claims it's a great value for the price:
https://riverheightsmusic.com/grote-guitars-review-7-string-arch-top/
Trembita (Ukraine)
7-string steel string
https://trembita-guitars.com/index
Leo Tone (Ukraine)
7-string steel string
https://www.amazon.com/Russian-Guitar-Acoustic-Classical-Cutaway/dp/B00L2K6DJY
Somewhat unfavorable review:
https://www.youtube.com/watch?v=NZd1b-yJqrs
Jackson Dinky
7-string electric
Mid-range (US$600-1500)
Ovation
Custom Elite 8-string steel string w pickup
Discontinued, try to buy one used, it used to retail for $1200-1600 new.
Agile / Rondo
various 7 and 8 strings
Ibanez
various models