ABSTRACT Coronal mass ejections (CMEs) may have major importance for planetary and stellar evolution. Stellar CME parameters, such as mass and velocity, have yet not been determined statistically. So far only a handful of stellar CMEs has been detected mainly on dMe stars using spectroscopic observations. We therefore aim for a statistical determination of CMEs of solar-like stars by using spectroscopic data from the ESO phase 3 and Polarbase archives. To identify stellar CMEs, we use the Doppler signal in optical spectral lines being a signature of erupting filaments that are closely correlated to CMEs. We investigate more than 3700 h of on-source time of in total 425 dF-dK stars. We find no signatures of CMEs and only few flares. To explain this low level of activity, we derive upper limits for the non-detections of CMEs and compare those with empirically modelled CME rates. To explain the low number of detected flares, we adapt a flare power law derived from EUV data to the H α regime, yielding more realistic results for H α observations. In addition, we examine the detectability of flares from the stars by extracting Sun-as-a-star H α light curves. The extrapolated maximum numbers of observable CMEs are below the observationally determined upper limits, which indicates that the on-source times were mostly too short to detect stellar CMEs in H α. We conclude that these non-detections are related to observational biases in conjunction with a low level of activity of the investigated dF-dK stars.