Are you looking for something like the following. If not, please post an example of your data as a Reproducible Example.
library(purrr)
#> Warning: package 'purrr' was built under R version 3.5.3
library(dplyr)
LIST <- list(A = data.frame(D = 1:6, B = rep(LETTERS[1:3], 2)),
C = data.frame(E = 2:7, B = rep(LETTERS[1:3], 2)))
LIST
#> $A
#> D B
#> 1 1 A
#> 2 2 B
#> 3 3 C
#> 4 4 A
#> 5 5 B
#> 6 6 C
#>
#> $C
#> E B
#> 1 2 A
#> 2 3 B
#> 3 4 C
#> 4 5 A
#> 5 6 B
#> 6 7 C
MyFunc <- function(DF) {
DF %>% group_by(B) %>%
mutate(NewCol = 1:n()) %>%
arrange(B)
}
LIST2 <- map(LIST, MyFunc)
LIST2
#> $A
#> # A tibble: 6 x 3
#> # Groups: B [3]
#> D B NewCol
#> <int> <fct> <int>
#> 1 1 A 1
#> 2 4 A 2
#> 3 2 B 1
#> 4 5 B 2
#> 5 3 C 1
#> 6 6 C 2
#>
#> $C
#> # A tibble: 6 x 3
#> # Groups: B [3]
#> E B NewCol
#> <int> <fct> <int>
#> 1 2 A 1
#> 2 5 A 2
#> 3 3 B 1
#> 4 6 B 2
#> 5 4 C 1
#> 6 7 C 2
Created on 2019-09-16 by the reprex package (v0.2.1)