According to recent new definitions, a multi-party behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. Three experimental results published in 2022 provide initial evidence, subject to postselection-related assumptions, for the existence of behaviors meeting these definitions of GMNL. The new definitions of GMNL differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources when classifying behaviors asonly bipartite nonlocal. I will discuss the interrelationships of these choices in three-party quantum networks, and present a behavior in the simplest nontrivial multi-partite measurement scenario (3 parties, 2 measurement settings, and 2 outcomes) that (A) cannot be simulated in a bipartite network prohibiting both entangled measurements and superquantum resources, (B) can be simulated with bipartite-only quantum states allowing for an entangled quantum measurement (indicating an approach to device independent certification of entangled measurements with fewer settings than in previous protocols), and surprisingly (C) can be simulated with bipartite-only superquantum states (Popescu-Rohrlich boxes) while maintaining a prohibition on entangled measurements. It turns out that other behaviors previously studied as device-independent witnesses of entangled measurements can also be simulated in the manner of (C), posing a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.