Chemical bonding between the Rydberg molecule NH4 and three alkali atoms Li, Na, and K, via their 2s, 3s, or 4s valence orbitals, is examined using flexible atomic orbital basis sets and high level ab initio methods. The results thus obtained suggest that (NH4)Na and (NH4)K should have large enough barriers to fragmentation (to (NH3) plus the alkali hydride) to be detected experimentally if it can be formed, but suggest that (NH4)Li has such a small barrier to render it impossible or much more difficult to observe. For all three species, minimum-energy structures, local harmonic vibrational frequencies, and plots of the Rydberg-valence bonding orbitals are given. The activation barriers separating these structures from their (NH4) plus alkali hydride fragments vary from 3 to 9 kcal/mol, while the energies required to dissociate to NH4 plus an alkali atom range from 9 to 16 kcal/mol.