[![enter image description here][1]][1]

**Create a Second Particle Surface**

---

  [1]: https://i.sstatic.net/3mVMN.png

In the image above the dark blue mesh on the left has a particle system with particles overlapping.  On the far right is a mesh with shape originating from the dark blue surface and showing faces and other spacing vertices.  The middle mesh shows a successful particle system with no overlap of particles.

 - Original Plane Exists.

 - New Plane.  Loop Cut in Both Directions Coarsely.  Place New Above Old.  Shrink Wrap Modfier with settings suited to your tastes.  Apply Shrink Wrap.  Now new plane has general shape of old with less vertices

 - New Plane in edit mode.  Face Selection Mode. Median Scale Mode. Select all. Extrude [Individual] Faces from Menu.  No Movement. Accept operation. Scale Small.  Invert Selection. Delete Faces Only.  You should be left with islands of faces as shown above.  Note this a very technical sequence of steps.  No artistic effort.

 - Inspect and Test.  If desired manually or randomly select from menu, more faces. Delete faces only.

 - You can also consider weight painting

 - Of course I may have left out some steps.  Please excuse those errors.

---