The thickness parameters that most empirical models use are generally defined by empirical relations related to ionogram characteristics. This is the case with the NeQuick model that uses an inflection point below the F2 layer peak to define a thickness parameter of the F2 bottomside of the electron density profile, which is named B2. This study is focused on the effects of geomagnetic storms on the thickness parameter B2. We selected three equinoctial storms, namely 17 March 2013, 2 October 2013 and 17 March 2015. To investigate the behavior of the B2 parameter before, during and after those events, we have analyzed variations of GNSS derived vertical TEC (VTEC) and maximum electron density (NmF2) obtained from manually scaled ionograms over 20 stations at middle and low latitudes of Asian, Euro-African and American longitude sectors. The results show two main kinds of responses after the onset of the geomagnetic events: a peak of B2 parameter prior to the increase in VTEC and NmF2 (in ~60% of the cases) and a fluctuation in B2 associated with a decrease in VTEC and NmF2 (~25% of the cases). The behavior observed has been related to the dominant factor acting after the CME shocks associated with positive and negative storm effects. Investigation into the time delay of the different measurements according to location showed that B2 reacts before NmF2 and VTEC after the onset of the storms in all the cases. The sensitivity shown by B2 during the studied storms might indicate that experimentally derived thickness parameter B2 could be incorporated into the empirical models such as NeQuick in order to adapt them to storm situations that represent extreme cases of ionospheric weather-like conditions.