Preventing overplotting for specific data points in ggplot2 scatterplot

I am trying find a way to prevent points in my ggplot2 scatterplot from overlapping whilst ideally not changing the position of the non-overlapping points (in this example, not moving points with the ids 1, 4, or 5). I would like to maintain the relative position of each of the points, but they can be moved slightly in the x and y as necessary.

library(ggplot2)

df <- data.frame(
  id = 1:9,
  x = c(1, 2, 2.1, 4, 5, 8.7, 9.1, 9, 8.9),
  y = c(10, 9, 9, 7, 6, 2.4, 2, 2.1, 2),
  size = rep(1:4, length.out = 9)
)

plot <- ggplot(df, aes(x = x, y = y)) +
  geom_point(aes(size = size), alpha = 0.8, shape = 21, color = "black") +
  geom_text(aes(label = id, size = 0.4*size), color = "black") +
  scale_size_area(max_size = 8) +
  xlim(1, 10) +
  ylim(1, 10) +
  theme_bw()

plot

Idea of ideal Scatterplot without overlapping points

I have tried position_jitter but to prevent overlap, I had to jitter all of the points so much that their relative positions were unrecognizable. I have also attempted position_dodge, however, as some points need to be moved in the x and some in the y to prevent overlap, I'd basically be doing this manually for 100 data points in my original dataset. I think something similar to the way geom_text_repel and geom_label_repel moves labels the minimum amount so they don't overlap would be ideal! Side note: this is my first post to stack overflow, apologies for any errors!!

The base plot function of R can utilize a jitter function as well which may suit your needs. Otherwise, I would recommend changing the transparency of your points in ggplot by adding

geom_point(alpha = 0.1)

Additionally, you could try changing the size of the points,

geom_point(size=1.5)

You could also try changing the color or shape of the points, but you would need another variable to determine what colors or shapes the points would be.