possibility of metallic ammonium In chemistry class, we discussed how metallic bonding occurs when metals lose electrons and become cations while the lose electrons become delocalized electrons and bind the metal cations. These electrons are then free to flow around the metal cations. But could the metal be replaced with an ammonium cation instead? (Or any other polyatomic cation, but we only learn ammonium and I'm not aware of any others minus hydronium which doesn't exist out of a solution.) Would the electrons still be free? How would you make it? And how could you prevent the following from occurring?
$$\ce{2NH4+ + 2e- -&gt; 2NH3 + H2}$$
A nomenclature note: conventionally, in chemistry "a metal" is an element (such as a transition metal or alkali metal). If what you're talking about is a substance that behaves as a metal, that's typically referred to as metallic, like metallic glasses. 

Therefore, I would rephrase your question as "Can metallic ammonium exist?" - in fact, this has been a question for quite awhile. From what I've read, there's a theoretical basis that it should be possible at given temperatures and pressures, but it hasn't been experimentally observed. The papers I was reading were from the 50s-70s, so I'll keep looking for more recent information. 

Solvated electrons are slightly related, in that there is a "free" electron, and this was in fact originally documented in liquid ammonia.