I personally find across kind of unintuitive and difficult to debug. nest is more intuitive. It will create a list of data frames with the contents.
iris %>%
nest(data = Sepal.Length:Petal.Width) %>%
mutate(result = map(data, function(x) colnames(x))) %>%
unnest(data)
Obviously in this example, the function is just getting the column names, but you can put your own function there.