I'm not sure what physics based puzzles have to do with a witches exam. Shouldn't mastery of magics be the key to success?
Oh no, I mean
physics-based gameplay. You know, like NightSky or Limbo. Realistic interaction with the environment/scenery. Here's an example:
The player and her pumpkin/ball come across a ditch filled with water that the witch can't cross (she doesn't have the water-walking spell yet.)
There's a weak-looking tree on the other side of the pit.
The player switches control to the pumpkin, bounces to the other side, and pushes the tree over the ditch by bouncing into it, creating a path for the witch to cross.
There will be other scenarios like where the witch has to push around boxes so the pumpkin can jump higher, and using the pumpkin itself as an stepping stone for the witch, and so on.
A big drawback I see is if it's Metroidvania, then you'll have to navigate to collaborative areas twice. Maybe, Mimi could carry Pumpum around. Or, maybe there could be stations where one character could summon the other.
This is what I was thinking.
The witch would get a Summon Familiar spell early in the game that teleports the pumpkin back to her. For balancing reasons maybe we could limit this spell to only work inside specially-placed pumpkin-patches? These could also work as save points.
Designing a large map that can be navigated and re-navigated as a witch and as a pumpkin will be a large challenge. In Knytt Underground there are many places which are easy for the the sprite to walk through but highly annoying to traverse as the ball. It sounds better suited to a level based design to me. A Mario-world map would allow for replaying levels with new abilities.
I'm picturing this game's world design as a mix of KU and WaDF: A single huge map divided into areas that can't be entered without specific abilities, along with some doors and portals that lead to self-contained "levels" as in WaDF.
At the center of the world will be the Witches School in the Witch Village. In the school there will be a chalkboard with a checklist of spells that Mimi has to learn before she can attempt the final exam. There'll also be a list of locations written on the board where each spell can be found, like: "Water-Walking spell - The Haunted Forest."
SO the player has to go each area, get new spells similar to how the ball gains new materials in WaDF, return to the school if needed, then go to the next area. Like WaDF there will be a balance of linearity and freedom to the order in which different areas can be visited. Some areas will require specific spells (like an island on the other side of a lake which can only be reached with the water-walking spell) and some areas will be accessible at all times.
The ultimate goal will be to return to the school after all spells have been collected, then enter the final level where Mimi has to use all those spells to pass.
Of course this is just my current vision, feel free to adapt and improvise as you see fit.