In vitro 3D cell models have been accepted to better recapitulate aspects of in vivo organ environment than 2D cell culture. Currently, the production of these complex in vitro 3D cell models with multiple cell types and microenvironments remains challenging and prone to human error. Here, a versatile ink comprising a 4-arm poly(ethylene glycol) (PEG)-based polymer with distal maleimide derivatives as the main ink component and a bis-thiol species as the activator that crosslinks the polymer to form the hydrogel in less than a second is reported. The rapid gelation makes the polymer system compatible with 3D bioprinting. The ink is combined with a novel drop-on-demand 3D bioprinting platform, designed specifically for producing 3D cell cultures, consisting of eight independently addressable nozzles and high-throughput printing logic for creating complex 3D cell culture models. The combination of multiple nozzles and fast printing logic enables the rapid preparation of many complex 3D cell cultures comprising multiple hydrogel environments in one structure in a standard 96-well plate format. The platform's compatibility for biological applications is validated using pancreatic ductal adenocarcinoma cancer (PDAC) and human dermal fibroblast cells with their phenotypic responses controlled by tuning the hydrogel microenvironment.