  Aims. The aim of our work is to analyze the light curves of $\beta$ Pic
recently observed by TESS in sectors 32, 33, and 34, searching for the
signatures of exocomet transits. Methods. We process the $\beta$ Pic light
curves from the MAST database, applying the frequency analysis to remove
harmonic signals due to the star's pulsations and use a simple 1-D model to fit
the profiles of the found events. Results. We recover events previously found
by other authors in sectors 5 and 6 and find five new distinct aperiodic
dipping events with asymmetric shapes resembling the expected profiles due to
the passage of a comet-like body across the star disk. These dips are rather
shallow, with the flux drop at a level of 0.03\% and a duration of less than 1
day. No periodic transits were found in the sectors investigated. Conclusions.
The depth and duration of the identified dips are similar to the recently
discovered transits in the $\beta$ Pic light curves from sector 5 of the TESS
observations as well as to those found in the light curves of KIC 354116 and
KIC 1108472 from the Kepler database. It indicates that aperiodic shallow dips
are not likely an exceptional phenomenon, at least for the $\beta$ Pic system.
