It may work for you?

library(dplyr)
df2 <- df |> group_by(x) |>
  summarise(y = max(y))

ggplot(df,aes(x,y), col = x) + 
  geom_point() +
  geom_point(data = df2,
             pch = 21, fill = "red", color = "black") +
  geom_line(data = specials, aes(x = positions, y = maxes))