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The modern study of astrophysical transients has been transformed by an exponentially growing volume of data. Within the last decade, the transient discovery rate has increased by a factor of ~20, with associated survey data, archival data, and metadata also increasing with the number of discoveries. To manage the data at this increased rate, we require new tools. Here we present YSE-PZ, a transient survey management platform that ingests multiple live streams of transient discovery alerts, identifies the host galaxies of those transients, downloads coincident archival data, and retrieves photometry and spectra from ongoing surveys. YSE-PZ also presents a user with a range of tools to make and support timely and informed transient follow-up decisions. Those subsequent observations enhance transient science and can reveal physics only accessible with rapid follow-up observations. Rather than automating out human interaction, YSE-PZ focuses on accelerating and enhancing human decision making, a role we describe as empowering the human-in-the-loop. Finally, YSE-PZ is built to be flexibly used and deployed; YSE-PZ can support multiple, simultaneous, and independent transient collaborations through group-level data permissions, allowing a user to view the data associated with the union of all groups in which they are a member. YSE-PZ can be used as a local instance installed via Docker or deployed as a service hosted in the cloud. We provide YSE-PZ as an open-source tool for the community.