As three-dimensional cell culture formats gain in popularity, there emerges a need for tools that produce vast amounts of data on individual cells within the spheroids or organoids. Here, we present a microfluidic platform that provides access to such data by parallelizing the manipulation of individual spheroids within anchored droplets. Different conditions can be applied in a single device by triggering the merging of new droplets with the spheroid-containing drops. This allows cell-cell interactions to be initiated for building microtissues, studying stem cells' self-organization, or observing antagonistic interactions. It also allows the spheroids' physical or chemical environment to be modulated, as we show by applying a drug over a large range of concentrations in a single parallelized experiment. This convergence of microfluidics and image acquisition leads to a data-driven approach that allows the heterogeneity of 3D culture behavior to be addressed across the scales, bridging single-cell measurements with population measurements.