I also want to mention that you can perform resistance training for the large toe, which I would assume might help with some of the moves in ballet that involve standing on the toes:
Br
Do you have a link for a video showing the jumps or demonstrating how they are performed?
I don't see a problem with deep squatting, in fact I would suggest it. I was avoid any isolated knee extension work though (leg extensions, etc.)
Br
I see. Ok, the medial hamstrings (semimembranosus and semitendinosis) and the adductors are creating the majority of the force. Sumo style deadlifts are a good exercise to improve that movement. And, when the dancer is strong and conditioned enough, adding a pull (or jump shrug) into the explosive sumo deadlift should really increase force production and jump height.
Thanks, okay. The reps would be in the low end then and tempo fairly fast, at least for the concentric part. Gaining muscle and weight is a concern (this is a female dancer), so I imagine keeping the set duration below 20 seconds would be a good idea?
Google Sefton Clarke. He is a strength coach who also teaches ballet.
There won't be a lot of people with greater first hand experience than him.
Yes, keep the training predominantly neural based: low reps, moderate weight, fast movements, moderate rest (1-3 min). I would also suggest following up with unilateral work, such as single leg rumanian dead lifts, rear foot elevated split squats, etc. These I would so for sets of 8-12. 1-2 sets should be sufficient to increase strength while keeping volume (and muscle gain) minimal.