For caustics to look better, you may want to try another render engine than "progressive" (see screenshot), Bidir and PPM seem to be the best working with caustics.
They DO have their limitations, though, Bidir seems to ignore volumetric effects, so it's inverse biblical (wine to water) in your renderings.
You also might want to (drastically) increase your MSI value (Max. Sample Intensity in the Performance Settings).
Improvements for caustics are on the roadmap for Max, so hopefully, they will come to C4D as well soon.