Double-Rydberg anions consist of a closed-shell cationic core and two electrons in diffuse orbitals. In addition to the already characterized tetrahedral NH4- and pyramidal OH3-, the list of stable double-Rydberg anions includes members of the NH3R- and OH2R- sets (where R = F, OH, NH2, and CH3) considered here. Double-Rydberg isomers of NH3OH-, NH3 NH2-, NH3CH3-, and OH2CH3- are stable minima in their potential energy surfaces and have positive, vertical electron detachment energies. Similar structures have been found for the corresponding neutrals, which all have adiabatic electron affinities that are greater than zero. Dyson orbitals pertaining to the least bound electrons of the NH3R and OH2R- anions are distributed chiefly outside the N-H and O-H bonds of the tetrahedral nitrogen and pyramidal oxygen atoms.