The electrostatically embedded many-body expansion (EE-MB), at both the second and third order, that is, the electrostatically embedded pairwise additive (EE-PA) approximation and the electrostatically embedded three-body (EE-3B) approximation, are tested for mixed ammonia-water clusters. We examine tetramers, pentamers, and hexamers for three different density functionals and two levels of wave function theory, We compare the many-body results to the results of full calculations performed without many-body expansions. Because of the differing charge distributions in the two kinds of monomers, this provides a different kind of test of the usefulness of the EE-MB method than was provided by previous tests on pure water clusters. We find only small errors due to the truncation of the many-body expansion for the mixed clusters. In particular, for tests on tetramers and pentamers, the mean absolute deviations for truncation at second order are 0.36-0.98 kcal/mol (average: 0.66 kcal/mol), and the mean absolute deviations for truncation at third order are 0.04-0.28 (average: 0.16 kcal/mol). These may be compared to a spread of energies as large as 4.24 kcal/mol in the relative energies of various structures of pentamers and to deviations of up to 8.57 kcal/mol of the full calculations of relative energies from the best estimates of the relative energies. When the methods are tested on hexamers, the mean unsigned deviation per monomer remains below 0.10 kcal/mol for EE-PA and below 0.03 kcal/mol for EE-3B. Thus the additional error due to the truncation of the expansion is small compared to the accuracy needed or the other approximations involved in practical calculations. This means that the EE-MB expansion in combination with density functional theory or wave function theory for the oligomers provides a useful practical model chemistry for making electronic structure calculations and simulations more affordable by improving the scaling with respect to system size.