How does it work the interaction between Magic jar and Find Steed?

Find steed spell describes:

…While mounted on your steed, you can make any spell you cast that targets only you also target your steed.

And, the spell Magic Jar is a "Self" range spell. How would this interaction work? Both your souls would go to the same container? Could you leave the container ending the spell on itself and keeping the steed on the container? Could you use two diferential container, one for you and one for the steed?