A series of low-density, multiprincipal component alloys containing high concentrations of Al, Mg, Li, Zn, Cu and/or Sn was designed using a strategy based on high-entropy alloys (HEAs). The alloys were prepared by induction melting under high-purity argon atmosphere, and the resulting microstructures were characterized in the as-cast condition. The resulting microstructures are multiphase and complex and contain significant volume fractions of disordered solutions and intermetallic compounds. By analyzing the atomic size difference, enthalpy of mixing, entropy of mixing, electronegativity difference, and valence electron concentration among the constituent elements, modified phase formation rules are developed for low-density multiprincipal component alloys that are more restrictive than previously established limits based on more frequently studied HEAs comprising mostly transition metals. It is concluded that disordered solid solution phases are generally less stable than competing ordered compounds when formulated from low-density elements including Al, Mg, and Li.