Due to the radical uncertainty associated with grand challenges prior studies have emphasized the need for robust action, which preserves future options while taking existing means and institutional constraints seriously. In this conversation on entrepreneurial futures and possibilities, we suggest that for such approaches to avoid merely reproducing or incrementally improving upon existing ideas and institutions, they must be underpinned by a set of cognitive practices that encourage the systematic interrogation of existing assumptions, the surfacing of bold systemic interventions, and efforts to discourage early dismissals of such interventions based on historically-grounded feasibility judgments. To encapsulate these cognitive practices, we introduce the concept of possibilistic thinking, noting how such thinking significantly reorients entrepreneurs’ attention and reasoning processes. We conclude by discussing the tensions associated with possibilistic thinking as well as opportunities for further research.