The climate of the Quaternary period is dominated by glacial–interglacial variability due to changes in the Earth's orbital parameters that control the incoming solar radiation. However, certain features of this variability remain puzzling. A notable example is the so-called Mid-Pleistocene Transition (MPT, ca. 1 million years ago), characterized by the shift of the predominant periodicity in climate variability from 40 kyr during the Early Pleistocene to 100 kyr at the Late Pleistocene. Previous studies have tried to explain its origin by invoking two main hypotheses. The first one is based on the observed decreasing trends in temperature and CO<inf>2</inf> throughout various climatic proxies. The second one, the regolith hypothesis, is based on the change in the basal friction regime of the Northern Hemisphere ice sheets via a progressive elimination of sediment layers above the continents. Here, we use the Physical Adimensional Climate Cryosphere mOdel (PACCO) to reproduce orbital-scale climate variability throughout the entire Pleistocene through a physical albeit simplified approach. We find that a sustained regolith removal is capable of changing the periodicity and amplitude of glacial cycles at the right timing of the MPT. The decreasing trends in CO<inf>2</inf> and temperature during the Pleistocene can be explained in our study as a consequence of a change in the size of the Northern Hemisphere ice sheets. We also analyze different insolation metrics and conclude that none of the usual formulations have an impact on the transition, but rather affect the periodicity power at the Early Pleistocene.