Ongoing large-scale optical time-domain surveys, such as the Zwicky Transient Facility (ZTF), are producing alerts at unprecedented rates. Analysis of transient sources has so far followed two distinct paths: archival analysis of data on transient sources at a time when they are no longer observable and real-time analysis at the time when the sources are first detected. The latter is the realm of alert brokers such as the Arizona-NOIRLab Temporal Analysis and Response to Events System (ANTARES). In this paper, we synthesize the two analysis paths and present a first systematic study of archival alert-broker data, focusing on extragalactic transients with multipeaked light curves identified in the ANTARES archive of ZTF alerts. Our analysis yields a sample of 37 such sources, including corecollapse supernovae (with two analogs of iPTF14hls), thermonuclear supernovae interacting with their surrounding circumstellar medium, tidal disruption events, luminous blue variables, and as yet unclassified objects. A large fraction of the identified sources is currently active, warranting allocation of follow-up resources in the immediate future to further constrain their nature and the physical processes at work.