Share classes can be very varied(such as preferred shares that get what's left after bond debt is paid off on bankruptcy) but generally what he's proposing(a coop-style one-head-one-vote class) is not common. Not sure if it's legal for US corporations or not(I could swear it is but in any case it's exceedingly rare). The usual principle is one-share-one-vote.

And, famously, Berkshire Hathaway