We consider the kinetics of an irreversible reaction at the sites of an infinite, uniform, 1D polymer chain with first and second nearest neighbor (nn) cooperative effects. The special cases with just nn cooperative effects, and with nn blocking and general second nn cooperative effects have previously been solved exactly. For the latter case, we present several new results for highly autoinhibitory and autocatalytic rates. The general problem cannot be solved exactly but we apply the techniques of the preceding paper, which for this process exploit a shielding property of quadruples of unreacted sites, to obtain approximate solutions. Various cooperativity regimes are considered.