Abstract Supersoft X-ray sources (SSSs) are characterized by their low effective temperatures and high X-ray luminosities. The soft X-ray emission can be explained by hydrogen nuclear burning on the surface of a white dwarf (WD) accreting at an extremely high rate. A peculiar ∼67 s periodicity (P 67) was previously discovered in the XMM–Newton light curves of the SSS CAL 83. P 67 was detected in X-ray light curves spanning ∼9 yr, but exhibits variability of several seconds on time-scales as short as a few hours, and its properties are remarkably similar to those of dwarf nova oscillations (DNOs). DNOs are short time-scale modulations (≲1 min) often observed in dwarf novae during outburst. DNOs are explained by the well-established low-inertia magnetic accretor (LIMA) model. In this paper, we show that P 67 and its associated period variability can be satisfactorily explained by an application of the LIMA model to the more ‘extreme’ environment in an SSS (eLIMA), contrary to another recent study attempting to explain P 67 and its associated variability in terms of non-radial g-mode oscillations in the extended envelope of the rapidly accreting WD in CAL 83. In the eLIMA model, P 67 originates in an equatorial belt in the WD envelope at the boundary with the inner accretion disc, with the belt weakly coupled to the WD core by an ∼105 G magnetic field. New optical light curves obtained with the Sutherland High-speed Optical Camera are also presented, exhibiting quasi-periodic modulations on time-scales of ∼1000 s, compatible with the eLIMA framework.