I just did an experiment that goes along these lines.

I had some sodium carbonate crashing, harmala seemed done precipitating (got a bunch quickly, then the solid layer stopped growing). However, the water was still cloudy. Poured off some of the cloudy water and added NaOH. The cloudiness crashed a lot faster than the remaining liquid in the original sodium carbonate jar.

Then I acidified the NaOH jar with the new precipitate. Nothing much seemed to go into solution at all. I think whatever was making the sodium carb solution cloudy was a contaminant that NaOH crashed quickly and "denatured" so that it would remain solid and separate out furing the acid step.