plotting – How to separate a plot into grids

I have made a plot using the built in function DensityPlot using the code below

DensityPlot((E^-(x^2 + 
      y^2)^2)^2 + ((E^-(x^2 + y^2)^2) (x^2 + y^2) Cos(
      2 Pi))^2, {x, -3, 3}, {y, -3, 3}, PlotTheme -> "Minimal", 
 PlotRange -> All, PlotPoints -> 50, ColorFunction -> "Rainbow")

Which generated this plot here
enter image description here

Now what I would like to is separate the plot into four grids (or n grids). The reason I would like to have these four grids, is that ultimately I would use the center point of each grid (some x,y value) and substitute it in a formula to get an ellipse for that grid. Hopefully the why, helps a bit.

I have tried reading the documentation online, but I have not been able to find anything that can help me with this specific task.

I appreciate your help