Thinking about a typical non-transition metal (calcium)

The formula for Calcium chloride is CaCl₂. Why is that? If you tried to make CaCl, (containing a Ca⁺ ion), the overall process is slightly exothermic. By making a Ca²⁺ ion instead, you have to supply more ionization energy, but you get out lots more lattice energy. There is much more attraction between chloride ions and Ca²⁺ ions than there is if you only have a 1+ ion. The overall process is very exothermic. Because the formation of CaCl₂ releases much more energy than making CaCl, then CaCl₂ is more stable - and so forms instead.

What about CaCl₃? This time you have to remove yet another electron from calcium. The first two come from the 4s level. The third one comes from the 3p. That is much closer to the nucleus and therefore much more difficult to remove. There is a large jump in ionization energy between the second and third electron removed. Although there will be a gain in lattice enthalpy, it is not anything like enough to compensate for the extra ionization energy, and the overall process is very endothermic. It definitely is not energetically sensible to make CaCl₃