Classical T Tauri stars are low-mass objects that are still accreting material from the surrounding circumstellar disk. The accretion process is essential in the formation of Sun-like stars and in setting the properties of the disk at the time when planet formation occurs. We constructed a complex data set in order to examine the accretion process of VW Cha, a classical T Tauri multiple system, with the aim of studying the physical origin of the photometric and spectroscopic variability of the system. The TESS space telescope observed VW Cha between 2019 April 22 and June 19, and we complemented these data with contemporaneous ground-based I CJHK-band photometric measurements. In addition, we obtained high-resolution optical spectra with the VLT/ESPRESSO and the 2.2 m/FEROS instruments. Analyzing these data, we found that the TESS light curve shows photometric variations on timescales from minutes to weeks with a peak-to-peak amplitude of ~0.8 mag. The near-infrared light curves follow the shape of the optical measurements; however, the peak-to-peak amplitudes are slightly increasing toward the longer wavelengths. We took spectra in both fainter and brighter photometric states of the system, allowing us to examine the origin of a photometric brightening event. Our results show that this brightening event can be explained by increased accretion. In addition, our spectroscopic data also suggest that the primary component of VW Cha is a spectroscopic binary, as was proposed in earlier works.