Observations of $z \gtrsim 6$ quasars provide information on the early phases of the most massive black holes (MBHs) and galaxies. Current observations, able to trace both gas and stellar properties, show that most MBHs at high redshift seem overmassive compared to the local population, in line with the elliptical galaxy population, or even above, thus implying a very rapid growth of these objects. To assess the physical conditions for such a rapid growth and explain the existence of a population of already mature MBHs when the Universe was less than 1~Gyr old, we here explore whether episodes of accretion above the Eddington limit can occur across cosmic epochs. By employing state-of-the-art high-resolution cosmological zoom-in simulations of a $z\sim 7$ quasar, where different accretion regimes are consistently included, together with their associated radiative and kinetic feedback, we show that super-Eddington phases can be sustained for relatively long time-scales (tens of Myr) and discuss how they affect the growth of MBHs. We also show, by means of a semi-analytic evolution, that the MBH spin remains relatively low during super-Eddington phases, and this would result in a lower feedback efficiency, hence a potentially faster growth that might then explain the overmassiveness of high-redshift MBHs.