Distributed constraint optimization (DCOP) has emerged as a useful technique for multiagent coordination. While previous DCOP work focuses on optimizing a single team objective, in many domains, agents must satisfy additional constraints on resources consumed locally (due to interactions within their local neighborhoods). Such resource constraints may be required to be private or shared for efficiency's sake. This paper provides a novel multiply-constrained DCOP algorithm for addressing these domains which is based on mutually-intervening search, i.e. using local resource constraints to intervene in the search for the optimal solution and vice versa. It is realized through three key ideas: (i) transforming n-ary constraints to maintain privacy; (ii) dynamically setting upper bounds on joint resource consumption with neighbors; and (iii) identifying if the local DCOP graph structure allows agents to compute exact resource bounds for additional efficiency. These ideas are implemented by modifying Adopt, one of the most efficient DCOP algorithms. Both detailed experimental results as well as proofs of correctness are presented.