We present the results of a Palomar Transient Factory (PTF) archival search for blue transients that lie in the magnitude range between "normal" core-collapse and superluminous supernovae (i.e., with -21 ≤ MR(peak)≤-19). Of the six events found after excluding all interacting Type IIn and Ia-CSM supernovae, three (PTF09ge, 09axc, and 09djl) are coincident with the centers of their hosts, one (10iam) is offset from the center, and a precise offset cannot be determined for two (10nuj and 11glr). All the central events have similar rise times to the He-rich tidal disruption candidate PS1-10jh, and the event with the best-sampled light curve also has similar colors and power-law decay. Spectroscopically, PTF09ge is He-rich, while PTF09axc and 09djl display broad hydrogen features around peak magnitude. All three central events are in low star formation hosts, two of which are E+A galaxies. Our spectrum of the host of PS1-10jh displays similar properties. PTF10iam, the one offset event, is different photometrically and spectroscopically from the central events, and its host displays a higher star formation rate. Finding no obvious evidence for ongoing galactic nuclei activity or recent star formation, we conclude that the three central transients likely arise from the tidal disruption of a star by a supermassive black hole. We compare the spectra of these events to tidal disruption candidates from the literature and find that all of these objects can be unified on a continuous scale of spectral properties. The accumulated evidence of this expanded sample strongly supports a tidal disruption origin for this class of nuclear transients.