A generalized family of Adversary Robust Consensus protocols is proposed and analyzed. These are distributed algorithms for multi-agents systems seeking to agree on a common value of a shared variable, even in the presence of faulty or malicious agents which are updating their local state according to the protocol rules. In particular, we adopt monotone joint-agent interactions, a very general mechanism for processing locally available information and allowing cross-comparisons between state-values of multiple agents simultaneously. The salient features of the proposed class of algorithms are abstracted as a Petri Net and convergence criteria for the resulting time evolutions formulated by employing structural invariants of the net.