Imperial cider experiment

I was telling one of my friends how I make cider from storebought juice, and how I backsweeten with concentrate, and why you can't really do that in the bottle, etc, and we got to talking. Here's the idea:

Start with a 5gal carboy with 3 gallons of treetop juice (est OG 1.050). Pitch a healthy dose of ale yeast with some nutrient, and allow that to ferment mostly to completion. Add 12oz of treetop juice concentrate (est OG 1.200-1.225). Allow this to ferment, and repeat. If a total of sixteen 12oz containers of concentrate are added, this will net 4.5gal of cider with an effective OG of 1.100-1.108 with the help of no sugar other than that which came from an apple.

Perhaps I should try this once with 1 gallon of juice and 5 cans of concentrate.

It might be interesting to try it with a small batch of only concentrate. Mix water and concentrate until you get an OG of ~1.090ish (unless you want to go higher). An entire pack of Notty should be plenty of yeast for a 1 gallon batch with that gravity. Hopefully, the ale yeast won't ferment it completely and leave you just below 1.020?

Complete fermentation is fine with me, I'll backsweeten in the keg to taste. With this method, the gravity will never be higher than 1.050. I am taking a page from the playbook of the Utopias cloners.