[PhiPsiRuss]

With regard to NIC (and similar fraternities,) it goes like this.

If a man
1) resigns,
2) and that resignation is accepted from that fraternity's appropriate (inter)national body in writing,
3) then there are no (inter)national rules of any fraternity, of which I'm aware, that would prevent him from joining another fraternity

Such circumstances are very rare, but it happens.

Locally, most fraternities would be very hesitant to pledge such a man, but it wouldn't be because of (inter)national rules.

If a man joins one fraternity, doesn't properly resign, and then joins another, if he is exposed, he will be expelled from both.