In the crystal structures of the title compounds, C6H10N3O2+·C7H5O3−·H2O, (I), C6H10N3O2+·C7H4NO4−·H2O, (II), and C6H10N3O2+·C4H5O6−·C6H9N3O2, (III), the 2-amino-4,6-dimethoxypyrimidinium cation [abbreviated as (MeO)2-Hampy+] interacts with the carboxylate group of the corresponding anion through a pair of nearly parallel N—H⋯O hydrogen bonds to form R22(8) ring motifs. In (I), the (MeO)2-Hampy+ cation is centrosymmetrically paired through a pair of N—H⋯N hydrogen bonds involving the 2-amino group and a ring N atom forming an R22(8) motif. In (II), inversion-related R22(8) motifs (amino–pyrimidine–carboxylate motifs) are further bridged by N—H⋯O hydrogen bonds on either side forming a DDAA array of quadruple hydrogen bonds. This array is extended further on either side by Owater—H⋯Omethoxy hydrogen bonds, resulting in an array of six hydrogen bonds ( ADDAAD). The water molecule plays a pivotal role, and five hydrogen-bonded fused rings are formed around the water molecule. In (III), the carboxy group of the tartrate anion interacts with the ring N atom and 2-amino group of the neutral (MeO)2-ampy molecule through N—H⋯O and O—H⋯N hydrogen bonds. There is also an intramolecular O—H⋯O hydrogen bond in the tartrate anion. In all three crystal structures, C—H⋯O hydrogen bonds are observed. [ABSTRACT FROM AUTHOR]