We use the Auriga cosmological simulations of Milky Way (MW)-mass galaxies and their surroundings to study the satellite populations of dwarf galaxies in $\Lambda$CDM. As expected from prior work, the number of satellites above a fixed stellar mass is a strong function of the mass of the primary dwarf. For galaxies as luminous as the Large Magellanic Cloud (LMC), and for halos as massive as expected for the LMC (determined by its rotation speed), the simulations predict about 3 satellites with stellar masses exceeding $M_*>10^5\, M_\odot$. If the LMC is on its first pericentric passage, then these satellites should be near the LMC and should have orbital angular momenta roughly coincident with that of the LMC. We use 3D positions and velocities from the 2nd data release of the Gaia mission to revisit which of the "classical" MW dwarf spheroidals could plausibly be LMC satellites. The new proper motions of the Fornax and Carina dwarf spheroidals place them on orbits closely aligned with the orbital plane of the Magellanic Clouds, hinting at a potential Magellanic association. Together with the Small Magellanic Cloud (SMC), this result raises to $3$ the number of LMC satellites with $M_*>10^5\, M_\odot$, as expected from simulations. This also fills the 12-mag luminosity gap between the SMC and the ultra-faints Hyi1, Car2, Hor1, and Car3, the few ultra-faint satellites confirmed to have orbits consistent with a Magellanic origin.