In How can we add magic to the game? Glazius comprehensively covers most magic systems and how to add them to Mouse Guard, at the end they give the option
Not A Dodge: Actual Magic Systems
..but this is beyond the realm of my experience. You'll have to author your own, maybe taking inspiration from some of the Burning Wheel magic systems you can find in the main game or the Codex. Just keep in mind the two concerns when you go customizing - how is this magic going to get help from the Guard, and is this magic adaptable enough to act on whatever scale the Guard needs it to?
But I don't have experience with Burning Wheel magic systems, or the newer Torchbearer.
I want to run a game where the intrepid guard mice can learn everything from simple light spells to fireball and beyond, even if the more impressive magic is only known by NPCs (at least initially!).
Is this something somebody has done, and if so how did you make it work in a game of Mouseguard?