Stable binary icosahedral quasicrystals (i-QCs) based on rare earth (RE) and cadmium are typically accessed by solution growth experiments, which operate in very narrow composition and temperature windows. Here, we present a procedure which allows study of peritectic reactions between approximant crystal (AC) phase and liquid yielding i-RECd and exemplify with i-GdCd and ternary variants where Cd is partially replaced by isovalent Zn (i-Gd(Cd,Zn)) or Mg (i-Gd(Cd,Mg)), or the 4f element Gd is replaced by nonmagnetic Y (i-(Gd,Y)Cd). The solubility limits for Zn and Mg substitution are about 10% and 20%, respectively, whereas Gd and Y show a complete solid solution behavior. We find that the peritectic decomposition temperature for i-GdCd is 390 degrees C, which is decreased when Gd is replaced by Y (i-YCd: 350 degrees C) and increased when Cd is replaced by Zn (i-Gd(Cd90Zn10): 440 degrees C), and especially by Mg (i-Gd(Cd80Mg20): 520 degrees C). Whereas substitution decisively alters the decomposition temperature (and hence stability) of the considered i-QCs, the decomposition temperature of the corresponding AC phases remains at around 700 degrees C. During the investigation of the pseudobinary phase diagrams Gd-(Cd95Zn5), Gd-(Cd90Zn10), and Gd-(Cd(80M)g(20)), faceted i-QCs grains with sizes up to 4 x 4 x 4 mm(3) could be isolated.