Cai’s Magic-focused Caladrius path
Train Black Magic to B early, then combine Caladrius, a Black Magonius mount, and Levin Sword for a Magic-focused build.
Original video: “Fire Emblem: Fortune's Weave—after testing, Cai should still take the magic route” | Qingzheng Game Player; additional training details come from RonaldDuck in the comments, endorsed by the creator's reply.
For a Magic-focused 
Cai, choose 
Caladrius with Black Magonius and 
Levin Sword. Train Black Magic B in advance.
Prepare Black Magic B early
Caladrius is a physical-magic hybrid unlocked on Cai's route, requiring Black Magic B. Train Black Magic early once you choose this route instead of waiting until the class change.
Pair the Black Magonius with Levin Sword
Black Magonius adds Magic growth, while Levin Sword turns Magic into weapon damage. Cai's Blaze Arts also scale with Magic, so improving it supports both Blaze Arts and the magic sword; you do not need to rely solely on black spells.