Male calico cats do exist, but they're very rare and IIRC always infertile.
In the musical Macavity has much less of a role.
IIRC, it goes like:
1. Old Deuteronomy disappears under mysterious circumstances
2. Bombularina (Taylor Swift cat) and Demeter (she's probably in the background of the movie somewhere) sing the Macavity song, suggesting that Macavity kidnapped him. Demeter is Macavity's ex.
3. Some of Macavity's scary street-cats usher "Old Deuteronomy" back BUT WAIT!! It's actually Macavity in disguise! He tries to kidnap Demeter, but the Jellicle cats chase Macavity & co away.
4. Rum Tum Tugger sings the Mister Mistofelees song and by the end of it Mister Mistofelees has conjured Old Deuteronomy back.
(As far as motivation for kidnapping Old Deuteronomy, it seems like it was just so Macavity could disguise himself AS Old Deuteronomy, so he could get close enough to Demeter to grab her.)
In the stage production Old Deuteronomy's rescue is explicitly magical. Mister Mistofelees prompts a background-singer cat to go under a sheet and when he whips it off it's Old Deuteronomy under there instead.