I have been a casual CS user for at least a year and a half. In putting together a particle system demo to figure out how to implement one in my main project, I gave up on trying to use one of CS's particle systems because the documentation for setting one up in code (rather than the loader) essentially does not exist, plus there is no indication of how any of the pieces work together. This led me to throw together a rudimentary particle system, even though ideally I'd like to use one of CS's systems.
So I get something like this. Very simple.

The only issue is that you can see some problems where one particle overlaps another from the camera's perspective. Instead of blending the pixels of one genmesh (particle) through to another, all transparency on one genmesh shows the thing mesh of the wall instead. This means you can basically see an outline around a quad where there are particles behind it.
I know this is not a problem unique to myself or my implementation, because in the vast majority of particle demos in CS you get the same effect. I have seen a small number of exceptions where this effect does not pop up and alpha blending is handled perfectly. I have tested several image types and approaches to transparency, as well as several mixmodes, and have not been able to achieve what I'm looking for.
My question is, how do I achieve the type of blending I am looking for? I know it's possible in CS, but I also know that some examples of effects suffer from the same issue.
Thanks for reading.