We present the light curves of the hydrogen-poor superluminous supernovae (SLSNe I) PTF 12dam and iPTF 13dcc, discovered by the (intermediate) Palomar Transient Factory. Both show excess emission at early times and a slowly declining light curve at late times. The early bump in PTF 12dam is very similar in duration (similar to 10 days) and brightness relative to the main peak (2-3 mag fainter) compared to that observed in other SLSNe I. In contrast, the long-duration (>30 days) early excess emission in iPTF 13dcc, whose brightness competes with that of the main peak, appears to be of a different nature. We construct bolometric light curves for both targets, and fit a variety of light-curve models to both the early bump and main peak in an attempt to understand the nature of these explosions. Even though the slope of the late-time decline in the light curves of both SLSNe is suggestively close to that expected from the radioactive decay of Ni-56 and Co-56, the amount of nickel required to power the full light curves is too large considering the estimated ejecta mass. The magnetar model including an increasing escape fraction provides a reasonable description of the PTF 12dam observations. However, neither the basic nor the double-peaked magnetar model is capable of reproducing the light curve of iPTF 13dcc. A model combining a shock breakout in an extended envelope with late-time magnetar energy injection provides a reasonable fit to the iPTF 13dcc observations. Finally, we find that the light curves of both PTF 12dam and iPTF 13dcc can be adequately fit with the model involving interaction with the circumstellar medium.