One possibility is to require of everybody to disclose real identity to the moderation team, with an option to disclose or not disclose it to everybody; rigorous formulation of rules about which kind of behaviour may then imply that the identity must become public is not necessary in my opinion.

(The comment by quid indicates I've been too fuzzy here so I'll try to detalize)

If I understand correctly the idea is that if a real person behind some sort of abuse might become publicly known this would likely reduce motivation to commit that abuse. In this case it is even more efficient not to reveal precise rules describing in which cases such public disclosure will take place: the rest of the users will not be concerned anyway. All that is needed is for the moderating team to be able to provide information about real identity of a user in case of any inquiry or even without it. When exactly to do this I think it is completely safe and even more efficient to leave them to decide in each case individually.

(Hope this was not even more fuzzy...)

If this requires lots of technical work, and not only on MO but on the whole SE network, still I believe it is worth it, because of several serious reasons already well explained in answers here.

In any case I think discriminating among "suspicious" and "nice" users by requiring different things from them is a very harmful idea.