[clause: 连 + [noun] + 都 + [predicate]],(更)何况 + [noun](呢)?
[clause],(更)何况 + [clause: extra reason]
何况 follows a statement about one case and introduces a second case where the same thing holds all the more: "let alone", "much less". The first clause often uses 连…都 for the case that should have been easy; 何况 then names the harder one, as a rhetorical question that needs no answer.
It also runs the other way: if something is true in the usual case, it's even more true in the special one.
更何况 is the same word with extra force.
At the head of a clause after an argument, 何况 adds one more reason that clinches it: "besides", "what's more". 又 or 也 often follows.
况且 also means "besides", but it only adds a reason. It can't do "let alone".