Synthetic development is a nascent field of research that uses the tools of synthetic biology to design genetic programs directing cellular patterning and morphogenesis in higher eukaryotic cells, such as mammalian cells. Synthetic genetic networks comprising cell-cell communications and morphogenesis effectors (e.g. adhesion) are generated and integrated into a cellular genome. Current design methods for these genetic programs rely on trial and error, which limit the number of possible circuits and parameter ranges that can be explored. By contrast, computational models act as rapid testing platforms, revealing the networks, signals, and responses required for achieving robust target structures. Here we introduce a computational framework, based on cellular Potts, where contact dependent cell-cell signaling networks and cellular responses can be chosen in a modular fashion. We represent and tune a number of recently described synthetic morphogenic trajectories in silico, such as those resulting in multilayered synthetic spheroids. Our parameters were tuned using a comparison with published in vitro experimental results. Our tuned parameters were then used to design and explore novel developmental trajectories for the formation of elongated and oscillatory structures. Here, multiple rounds of optimization suggested critical parameters for the successful implementation of these trajectories. The framework that we develop here could function as a testing ground to explore how synthetic biology tools can be used to create particular multicellular trajectories, as well as for understanding both imagined and extant developmental trajectories.