Extract elements common in all column groups

by

First, split the df$ID by Month and use intersect to find elements common in each sub-group.

Reduce(intersect, split(df$ID, df$Month))
#[1] 4 6

If you want to subset the corresponding data.frame, do

df[df$ID %in% Reduce(intersect, split(df$ID, df$Month)),]

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