Overlay two ggplot2 stat_density2d plots with alpha channels

Here is exactly the same solution than @Roland, excepting that I suggest controur line. This allow you to appreciate the overlapping. I can't see how geom_tile and your idea of "multiplication" could enable you to appreciate that. Maybe if you use blue and red for none-overlapping area, and a "weighted" violet color for overlapping area. But I guess you would have to compute it in a previous step before ploting I guess.

contour_line

ggplot(rbind(data.frame(data, group="a"), data.frame(data2, group="b")), 
       aes(x=x,y=y)) + 
  stat_density2d(geom="density2d", aes(color = group,alpha=..level..),
                 size=2,
                 contour=TRUE) + 
  #scale_color_manual(values=c("a"="#FF0000", "b"="#00FF00")) +
  geom_point() +
  theme_minimal() +
  xlim(-3.3, 3.3) + ylim(-3.3, 3.3) +
  coord_cartesian(xlim = c(-3.2, 3.2), ylim = c(-3.2, 3.2))

You should plot both densities on the same scale:

ggplot(rbind(data.frame(data, group="a"), data.frame(data2, group="b")), 
       aes(x=x,y=y)) + 
  stat_density2d(geom="tile", aes(fill = group, alpha=..density..), 
                 contour=FALSE) + 
  scale_fill_manual(values=c("a"="#FF0000", "b"="#00FF00")) +
  geom_point() +
  theme_minimal() +
  xlim(-3.3, 3.3) + ylim(-3.3, 3.3) +
  coord_cartesian(xlim = c(-3.2, 3.2), ylim = c(-3.2, 3.2))

enter image description here