Lego is a fascinating case study. They've gone entirely corporate - so many of their expensive new products are branded partnerships. I guess it had to be done. There must be an HBS case study, or several, about this.
Brick by Brick is a great book about the history of Lego and how it came back from near bankruptcy. It reads like a business case study—turns out they were saved by a McKinsey consultant.
I wouldn't be surprised if branded partnerships have minimal profit and are mostly intended to keep a premium market perception.
Lego was pretty famous for doing branded partnerships and still struggling [1]. This lead them to come up with more of their own IP like Bionicle and Ninjago.
https://en.m.wikipedia.org/wiki/Jørgen_Vig_Knudstorp