  Recent discovery of many dwarf satellite galaxies in the direction of the
Small and Large Magellanic Clouds (SMC and LMC) provokes questions of their
origins, and what they can reveal about galaxy evolution theory. Here, we
predict the satellite stellar mass function of Magellanic Cloud-mass host
galaxies using abundance matching and reionization models applied to the
\textit{Caterpillar} simulations. Specifically focusing on the volume within
$50$~kpc of the LMC, we predict a mean of 4-8 satellites with stellar mass $M_*
> 10^4\, \mathrm{M_\odot}$, and 3-4 satellites with $80 < M_* \leq 3000\,
\mathrm{M_\odot}$. Surprisingly, all $12$ currently known satellite candidates
have stellar masses of $80 < M_* \leq 3000\, \mathrm{M_\odot}$. Reconciling the
dearth of large satellites and profusion of small satellites is challenging and
may require a combination of a major modification of the \mstarmhalo
relationship (steep, but with an abrupt flattening at $10^3\,
\mathrm{M_\odot}$), late reionization for the Local Group ($z_{\rm{reion}}
\lesssim 9$ preferred), and/or strong tidal stripping. We can more robustly
predict that $\sim 53\%$ of satellites within this volume were accreted
together with the LMC and SMC, and $\sim 47\%$ were only ever Milky Way
satellites. Observing satellites of isolated LMC-sized field galaxies is
essential to placing the LMC in context, and to better constrain the
\mstarmhalo relationship. Modeling known LMC-sized galaxies within $8$ Mpc, we
predict 1-6 (2-12) satellites with $M_* > 10^5\, \mathrm{M_\odot}$ ($M_* >
10^4\, \mathrm{M_\odot}$) within the virial volume of each, and 1-3 (1-7)
within a single $1.5^{\circ}$ diameter field of view, making their discovery
likely.
