ggplot : multiple lines starting from the same point

I have a dataset like this one :

df <- data.frame(Species = c("Sp A", "Other sp", "Other sp", "Other sp",
                       "Sp A", "Other sp", "Other sp"), 
           Study = c("A", "A", "A", "A", 
                     "B", "B", "B"), 
           Value = c(1, 3, 4, 5, 3, 6, 7))

Looks like this :

> df
   Species Study Value
1     Sp A     A     1
2 Other sp     A     3
3 Other sp     A     4
4 Other sp     A     5
5     Sp A     B     3
6 Other sp     B     6
7 Other sp     B     7

I would like to compare the values of the species A to the values of the other species from a same study.
This is the plot I have now :

ggplot(df, aes(y = Value, x = Species)) + 
    geom_point(shape = 1) +
    geom_line(aes(group = Study), color = "gray50") +
    theme_bw()

I don't want the vertical lines. Instead of this, I would like to have 5 lines, 3 starting from the lower "Sp A" point toward the 3 corresponding "Other sp" points from the same study (A) and 2 starting from the upper "Sp A" toward the 2 other points from the same study (B).