Intersectionality scholarship clearly sets out the limits of additive and multiplicative approaches to grasp the complex architecture of power. Yet, with respect to how the relationship between different components of this architecture is theorized, the study needs to be pursued and complexified. To this end, the article deploys the work of Stuart Hall and identifies and discusses two generative avenues for expanding and renewing theoretical frameworks of intersectionality. It proposes to: 1. combine Hall’s theory of articulation between different instances (economic / juridical-political / ideological) with the intersectional premise of the co-constitution of different operators of power (race / class / gender) in order to develop a more complex theory of power; and 2. rely on Hall’s theorisation of the conjuncture to avoid the pitfalls of a universal application of intersectionality and to grasp the geo-historical specificities of the ways articulations (economic / juridical-political / ideological) and intersections (race / class / gender) mutually constitute and form a differentiated complex unity, a “structure articulated in dominance” yet contingent.