Spatiotemporal optical vortex (STOV) wavepacket carrying transverse photonic orbital angular momentum (OAM) has been extensively studied in the past few years. In this Letter, we propose and study a novel STOV wavepacket with multiple phase singularities embedded in different space–time domains using analytical and numerical approaches. By tuning different parameters used for designing the wavepacket, it is possible to engineer both the magnitude and orientation of the photonic OAM in space–time. The vectorially controllable OAM will pave new avenues and facilitate applications such as novel optical communication, studying complicated quantum systems, and spin-and-OAM interactions.