  We present a study of the dielectric, structural, and magnetic properties of
the multiferroic or linear magnetoelectric substitution series
[(NH$_4$)$_{1-x}$K$_x$]$_2$[FeCl$_5$(H$_2$O)]. 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 ($x \le 0.06$) to a linear magnetoelectric ($x \ge 0.15$) 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.
