One of the sources of solar energetic particle (SEP) events is shocks that are driven by fast coronal mass ejections (CMEs). They can accelerate SEPs up to relativistic energies and are attributed to the largest SEP events. New studies suggest that CME-driven shocks can potentially accelerate electrons to MeV energies in the vicinity of the Sun. We focus on relativistic electrons associated with strong IP shocks between 2007 and 2019 to determine whether the shocks can keep accelerating such electrons up to 1 AU distance. We have analyzed High Energy Telescope (HET) observations aboard the STEREO spacecraft of potential electron energetic storm particle (ESP) events, characterized by intensity time series that peak at the time of, or close to, the associated CME-driven shock crossing. We present a new filtering method to assess the statistical significance of particle intensity increases and apply it to MeV electron observations in the vicinity of interplanetary shocks. We identified 27 candidate events by visual inspection from a STEREO in-situ shock list. Our method identified nine clear cases, where a significant increase of MeV electrons was found in association with a shock. Typically, the highest statistical significance was observed in the highest HET energy channel of electrons. All nine cases were associated with shocks driven by interplanetary CMEs that showed large transit speeds, in excess of 900 km/s. In several cases multiple shocks were observed within one day of the shock related to the electron increase. Although electron ESP events at MeV energies are found to be rare at 1 AU our filtering method is not designed to identify a potential interplanetary shock contribution from distances closer to the Sun. Future observations taken during closer approaches to the Sun will likely provide clarity on interplanetary shock acceleration of electrons.