A series of iron arsenides (e.g., CaRbFe4As4, SrCsFe4As4) have been discovered recently, and have provoked a rise in superconductor searches in a different phase, known as the 1144 phase. For the presence of various chemical substitutions, it is believed that more 1144 compounds remain to be discovered. In this work, we perform general model analysis as well as scenario calculation on a basis of density functional theory to investigate phase stability in a variety of compounds. We predict that the 1144-type phase could be stabilized in EuKFe4As4, EuRbFe4As4, EuCsFe4As4, CaCsFe4P4, SrCsFe4P4, BaCsFe4P4, InCaFe4As4, InSrFe4As4, etc. Remarkably, it involves rare earths, trivalence elements (e.g., indium) and iron phosphides, which greatly expands the range of its existence and suggests a promising prospect for experimental synthesis. In addition, we find that the formation of many random doping compounds (e.g., Ba0.5Cs0.5Fe2As2, Ba0.5R0.5Fe2As2) is driven by entropy and could be annealed to a 1144-type phase. Eventually, we plot a phase diagram about two structural factors Delta a and Delta c, giving a bird's-eye view of stability of various 1144 compounds.