In RD designs with multiple cutoffs, the identification of an average causal effect across cutoffs may be problematic if a marginally exposed subject is located exactly at each cutoff. This occurs whenever a fixed number of treatment slots is allocated starting from the subject with the highest (or lowest) value of the score, until exhaustion. Exploiting the "within" variability at each cutoff is the safest and likely efficient option. Alternative strategies exist, but they do not always guarantee identification of a meaningful causal effect and are less precise. To illustrate our findings, we revisit the study of Pop-Eleches and Urquiola (2013).