Penance strategy game theory
I see two ways to produce histories with multi-state deviations (not including the degenerate case in which all states defect):


Multiple states defect in different periods.  This possibility is ruled out so long as Equation 3 (the necessary and sufficient condition for unilateral defection at time $t-1$ to be punished by all other states at time $t$) is satisfied - in that case, only one state can ever defect at a time because all other states have credibly committed to Penance.
Multiple states defect in the same period. There are two obvious ways this can happen: 1) regional agreements are in effect and one of the regions is punishing a defection.  Equation 7 gives the conditions required for both regions to revert to Regional Penance in the following period, so this case isn't interesting.


The other way to have multiple states defect in the same period is the interesting case. It implies collusion between a subset of states. This reduces to the Regional Penance case if the subset is equal to half the states.  If it isn't, Footnote 10 explains that such an arrangement is not weakly renegotiation-proof. This makes sense, as collusion implies that (Regional) Penance is not, in fact, subgame perfect.