Touchscreens are the predominant medium for interactions with digital services; however, their current fixed form factor narrows the scope for rich physical interactions by limiting interaction possibilities to a single, planar surface. In this paper we introduce the concept of PickCells, a fully re-configurable device concept composed of cells, that breaks the mould of rigid screens and explores a modular system that affords rich sets of tangible interactions and novel across-device relationships. Through a series of co-design activities – involving HCI experts and potential end-users of such systems – we synthesised a design space aimed at inspiring future research, giving researchers and designers a framework in which to explore modular screen interactions. The design space we propose unifies existing works on modular touch surfaces under a general framework and broadens horizons by opening up unexplored spaces providing new interaction possibilities. In this paper, we present the PickCells concept, a design space of modular touch surfaces, and propose a toolkit for quick scenario prototyping.