dodge or jitter only at overlaps in ggplot2

I wold like to make a plot in ggplot2 with the values aligned to the center but dodged at the overlaps, like this one (done in graphpad prism)

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What I can do in ggplot2 with jitter looks like this

df<-data.frame(response=c(-0.3502294,0.4207441,0.1001638,-0.2401336,-0.2604142,0.4574286,
       0.755964,0.9241669,0.8212376,2.037581,0.6440635,0.2714898,1.433149,0.4627742,
       0.5639637,0.1610219,0.1516505,-1.322015,-0.2134711,0.8554756,0.400872,1.344739,
       0.3743637,0.6329151,0.1467015,0.6313575,0.3989693,0.1940468,-0.06594919,-0.1951204),
    group=c(rep("A",10),rep("B",10),rep("C",10)))

set.seed(1234)
ggplot(df,aes(group,response,fill=group))+
  geom_point(size=5,pch=21,position=position_jitter(w=.2))+
  scale_y_continuous(limits=c(-2,3))

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How can I keep the points aligned to the center and dodge only at the overlaps in ggplot2?