SkyPortal is an open-source software package designed to discover interesting transients efficiently, manage follow-up, perform characterization, and visualize the results. By enabling fast access to archival and catalog data, crossmatching heterogeneous data streams, and the triggering and monitoring of on-demand observations for further characterization, a SkyPortal-based platform has been operating at scale for >2 yr for the Zwicky Transient Facility Phase II community, with hundreds of users, containing tens of millions of time-domain sources, interacting with dozens of telescopes, and enabling community reporting. While SkyPortal emphasizes rich user experiences across common front-end workflows, recognizing that scientific inquiry is increasingly performed programmatically, SkyPortal also surfaces an extensive and well-documented application programming interface system. From back-end and front-end software to data science analysis tools and visualization frameworks, the SkyPortal design emphasizes the reuse and leveraging of best-in- class approaches, with a strong extensibility ethos. For instance, SkyPortal now leverages ChatGPT large language models to generate and surface source-level human-readable summaries automatically. With the imminent restart of the next generation of gravitational-wave detectors, SkyPortal now also includes dedicated multimessenger features addressing the requirements of rapid multimessenger follow-up: multitelescope management, team/group organizing interfaces, and crossmatching of multimessenger data streams with time-domain optical surveys, with interfaces sufficiently intuitive for newcomers to the field. This paper focuses on the detailed implementations, capabilities, and early science results that establish SkyPortal as a community software package ready to take on the data science challenges and opportunities presented by this next chapter in the multimessenger era.