This is rife with peril if the data.frame has other columns (there, I said it!), but the do block will allow you to generate a derived data.frame within a dplyr pipe (though, ceci n'est pas un pipe):
library(dplyr)
df <- data.frame(column = letters[1:4], stringsAsFactors = FALSE)
df %>%
do( data.frame(column = rep(.$column, each = 4), stringsAsFactors = FALSE) )
# column
# 1 a
# 2 a
# 3 a
# 4 a
# 5 b
# 6 b
# 7 b
# 8 b
# 9 c
# 10 c
# 11 c
# 12 c
# 13 d
# 14 d
# 15 d
# 16 d
As @Frank suggested, a much better alternative could be
df %>% slice(rep(1:n(), each=4))