In this article, we introduce the Intersectionally Conscious Collaboration (ICC) protocol to physics educators who seek to disrupt the long-standing inequities in their field. Recent studies raise awareness of diversity and inclusivity concerns and propose best practices for reducing bias toward women, LGBTQ+ students, and racially/ethnically minoritized students. Documented evidence demonstrates persistent challenges for women in physics in university settings, even addressing the identities and experiences of Women of Color. Simone Hyater-Adams and colleagues' Critical Physics Identity framework, focused on Black physics identity, simultaneously considers racial and physics identities and individuals' experiences within the context of structural and institutionalized oppression in the physics community. The ICC protocol includes six elements designed to support collaboration and inclusive instructional practices that respond to how multidimensional inequities and power differentials may manifest in academic settings.