In this contribution I examine digital technoscientific socialities through ethnographic fieldwork with Health for All, an interdisciplinary network formed at the start of the Covid‐19 outbreak. I expand the entangled commons framework for anthropological inquiry into collaborative, data‐intensive science, arguing that digital technoscientific socialities—not merely data—constitute entangled commons situated in the sociomateriality of knowledge coproduction. Focusing on mental health research in Italy, I explore tensions between open and proprietary data to reveal how data are never inert units but embedded in social relations. I argue that achieving multidimensional health notions requires open care to attend simultaneously to knowledge subjects, processing tools and infrastructures, rather than relying solely on data accumulation.