If you don't know, I got this idea from a line of games known as "super robot wars". It's a game franchise that involves a bunch of Mecha animr series and makes them all tied together and Make them go together to fight some bigger bad guy. but do keep in mind that despite the game original enemies, events from characters show do happen in game.bJust with a few different context because of more players being involved. For example as to what they do:

Crossover stuff. Character from different shows existing in one universe, with all the good and bad that brings (all their bad guys and big bads are in as well).

Canon welding. When stuff from different shows are treated as similar things. Where they basically write it so that powers from different series came the same thing for example.

Technology. When tech from different universe is treated as the same. 

Lore. Connecting different universe lore into one connected lore. Like Let's say that there were robots that had similar abilities to warp reality,  they would all be connected through the term >!Majine!< because of their reality manipulating power.

Characters. Turning, or making different characters connected, or twist them into one person.

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Since there is also an abundance of magical girls, I got curious and wondered what a: "Magical girl wars" would be like.

So tell me your thoughts and what you would come up with.

Let's say you (yes, you!) Were assigned to make a crossover video game with a bunch of magical girl shows. What shows are you using? And how would you tie their lore together? And what would the story be?