China’s growing influence in world politics has resurfaced old debates about hegemonic disputes over global order. At the core of these debates is the question of how the rise of China will interplay with the United States’ preponderant position in the international order and whether it may trigger hegemonic competition. Although hegemonic order studies have long focused on how powerful states build the institutions that underpin international order, they have little to say about how concomitant order-building efforts may shape the dynamics of conflict or cooperation among hegemons. Hegemonic interactions are assumed to be intrinsically conflict-prone and left under the states-under-anarchy framework. This paper argues that hierarchical relations among states constitute hegemonies and structure international orders. It proposes a network-relational framework for investigating the interplay among hegemonic efforts in order-building. Networked hierarchies can entangle multiple hegemonies together and constrain the pathways for cooperation and competition among hegemons. To demonstrate this framework’s utility, I apply it to a comparative analysis of the United States and Soviet Union’s competition in the Cold War (1950–1991) and the hegemonic-ordering dynamics ensuing from the rise of China (2006–2014).