Are there limits on the number of unique polygons created by the QGIS Union tool?

Is there a limit on the number of polygons that the Union tool will compute? I have overlapping radii from a variety of sources pictured below, but the tool continues to give me an "GEOS geoprocessing error: intersection failed" error every time I try with a larger dataset.

I’ve tried to fix geometries and checked validities for topology, are my overlaps just too numerous so the tool fails? Is there anything I can try, other than splitting my data into smaller and smaller peices and Unioning them individually until I get my final solution?