We present the results of our study of ASASSN-14dx, a previously known but poorly characterized cataclysmic variable (CV). The source was observed as part of an ongoing high-time-resolution photometric survey of CVs, which revealed that, in addition to the known 82.8-min orbital period, it also exhibits other transient periods, the strongest of which around 4 and 14 min. Here, we report our findings resulting from a multifaceted follow-up programme consisting of optical spectroscopy, spectropolarimetry, imaging polarimetry, and multicolour fast photometry. We find that the source displays complex optical variability, which is best explained by the presence of a massive white dwarf exhibiting non-radial pulsations. An intermediate polar-like scenario involving a spinning magnetic white dwarf can be ruled out based on the detected changes in the observed periods. Based on our optical spectroscopy, we can constrain the mass and effective temperature of the white dwarf to be similar to 1.1 M_☉ and 16 100 K, respectively. The overall intrinsic flux level of the source is unusually high, suggesting that there remains significant residual emission from the accretion disc and/or the white dwarf even ten years after the 2014 outburst. Finally, we cannot detect any spectroscopic signatures from the donor star, making ASASSN-14dx a possible period bouncer system evolving towards a longer orbital period.