We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish task objectives. We first ground our framework in sociocultural positions on disciplinary learning as educated perception. Next, we present and analyze empirical findings from three pilot studies of CGPC designs, where participants' multimodal discursive efforts to coordinate their actions resulted in cognitively productive outcomes that we characterize as revealing either substitution, mutuality, or synergy of perceptions.