This study shows that the intergenerational transmission of inequality in most of the 28 EU countries is higher than what a parent-to-child paradigm would suggest. While a strand of the literature claims that this is due to a direct grandparental effect, economic historian Gregory Clark maintains that multigenerational mobility follows a Markovian process. In his view, previous estimates of social status persistence are not only (severely) attenuated by an errors-in-variables problem, but are also constant across time and space. Using a survey covering all 28 EU countries, we provide evidence against such a "universal law of mobility". We show that, while in most EU countries traditional estimates of social status persistence are indeed downward biased, there are sizable differences across countries driven by country-specific factors. Further, for a few EU countries we cannot reject the hypothesis of a direct grandparental effect after accounting for a number of parents related covariates possibly affecting the multigenerational transmission process.