  Even though compressible plasma turbulence is encountered in many
astrophysical phenomena, its effect is often not well understood. Furthermore,
direct numerical simulations are typically not able to reach the extreme
parameters of these processes. For this reason, large-eddy simulations (LES),
which only simulate large and intermediate scales directly, are employed. The
smallest, unresolved scales and the interactions between small and large scales
are introduced by means of a subgrid-scale (SGS) model. We propose and verify a
new set of nonlinear SGS closures for future application as an SGS model in LES
of compressible magnetohydrodynamics (MHD). We use 15 simulations (without
explicit SGS model) of forced, isotropic, homogeneous turbulence with varying
sonic Mach number $\mathrm{M_s} = 0.2$ to $20$ as reference data for the most
extensive \textit{a priori} tests performed so far in literature. In these
tests we explicitly filter the reference data and compare the performance of
the new closures against the most widely tested closures. These include
eddy-viscosity and scale-similarity type closures with different
normalizations. Performance indicators are correlations with the turbulent
energy and cross-helicty flux, the average SGS dissipation, the topological
structure and the ability to reproduce the correct magnitude and direction of
the SGS vectors. We find that only the new nonlinear closures exhibit
consistently high correlations (median value \textgreater$0.8$) with the data
over the entire parameter space and outperform the other closures in all tests.
Moreover, we show that these results are independent of resolution and chosen
filter scale. Additionally, the new closures are effectively coefficient-free
with a deviation of less than $20\%$.
