We present the light curves of the hydrogen-poor superluminous supernovae (SLSNe-I) PTF12dam and iPTF13dcc, 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 PTF12dam is very similar in duration (~10 days) and brightness relative to the main peak (2-3 mag fainter) compared to those observed in other SLSNe-I. In contrast, the long-duration (>30 days) early excess emission in iPTF13dcc, 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 light-curve decline in both SLSNe is suggestively close to that expected from the radioactive decay of $^{56}$Ni and $^{56}$Co, 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 PTF12dam observations. However, neither the basic nor the double-peaked magnetar model is capable of reproducing the iPTF13dcc light curve. A model combining a shock breakout in an extended envelope with late-time magnetar energy injection provides a reasonable fit to the iPTF13dcc observations. Finally, we find that the light curves of both PTF12dam and iPTF13dcc can be adequately fit with the circumstellar medium (CSM) interaction model.
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