We present and discuss the optical spectrophotometric observations of the nearby (z = 0.087) Type I superluminous supernova (SLSN I) SN 2017gci, whose peak K-corrected absolute magnitude reaches M-g = -21.5 mag. Its photometric and spectroscopic evolution includes features of both slow- and of fast-evolving SLSN I, thus favoring a continuum distribution between the two SLSN-I subclasses. In particular, similarly to other SLSNe I, the multiband light curves (LCs) of SN 2017gci show two re-brightenings at about 103 and 142 d after the maximum light. Interestingly, this broadly agrees with a broad emission feature emerging around 6520 angstrom after similar to 51 d from the maximum light, which is followed by a sharp knee in the LC. If we interpret this feature as H alpha, this could support the fact that the bumps are the signature of late interactions of the ejecta with a (hydrogen-rich) circumstellar material. Then we fitted magnetar- and CSM-interaction-powered synthetic LCs on to the bolometric one of SN 2017gci. In the magnetar case, the fit suggests a polar magnetic field B-p similar or equal to 6 x 10(14) G, an initial period of the magnetar P-initial similar or equal to 2.8 ms, an ejecta mass M-ejecta similar or equal to 9M(circle dot) and an ejecta opacity kappa similar or equal to 0.08 cm(2) g(-1). A CSM-interaction scenario would imply a CSM mass similar or equal to 5 M-circle dot and an ejecta mass similar or equal to 12M(circle dot). Finally, the nebular spectrum of phase + 187 d was modeled, deriving a mass of similar or equal to 10 M-circle dot for the ejecta. Our models suggest that either a magnetar or CSM interaction might be the power sources for SN 2017gci and that its progenitor was a massive (40 M-circle dot) star.