We present a study of the dielectric, structural, and magnetic properties of the multiferroic or linear magnetoelectric substitution series [(NH4)1−xKx]2[FeCl5(H2O)]. Pyroelectric currents, magnetic susceptibilities, and thermodynamic properties were examined on large single crystals of the erythrosiderite compounds and detailed magnetic-field versus temperature phase diagrams are derived for three different substitution levels. With increasing potassium concentration the material is tuned from a multiferroic (x ≤ 0.06) to a linear magnetoelectric (x ≥ 0.15) ground state. In contrast to the respective pure parent compounds with x = 0 or 1, however, the ferroelectric or linear magnetoelectric polarization in none of the substituted samples is switchable by external electric fields, because these samples exhibit a significant electric polarization already above the magnetic ordering transition. The polarization arises at a higher-lying structural phase transition that is examined by THz spectroscopy and, on a deuterated pure single crystal, by comprehensive neutron-diffraction experiments. The structural phase transition is attributed to an ordering of NH + 4 tetrahedra but does not break inversion symmetry in the pure material, while a finite K content causes pyroelectricity.