This is a little vague, and I've not tried it myself. But may be worth a shot...

Create a copy of your feature class (say, 'fcCopy'). Then run an intersect on the 'fc' original feature class, and the 'fcCopy' feature class.

Now you can select overlapping polygons from the intersection where 'OBJECTID_fc <> OBJECTID_fcCopy'.

Copy these overlapping polygons out to a new feature class.

Dissolve the new feature class.

Replace the overlapping features in the original feature class with the dissolved ones if desired.

(This idea comes from one of the answers at: https://community.esri.com/thread/7714 )

It may require some further complication for overlapping features that are adjacent to other overlapping features, to avoid dissolving with them. In this case, you may need to do the export/dissolve separately for each pair of overlapping features.

This is a little vague, and I've not tried it myself. But may be worth a shot...

Create a copy of your feature class (say, 'fcCopy'). Then run an intersect on the 'fc' original feature class, and the 'fcCopy' feature class.

Now you can select overlapping polygons from the intersection where 'OBJECTID_fc <> OBJECTID_fcCopy'.

Export these overlapping polygons out to a new feature class.

Dissolve the new feature class.

Replace the overlapping features in the original feature class with the dissolved ones if desired.

(This idea comes from one of the answers at: https://community.esri.com/thread/7714 )

It may require some further complication for overlapping features that are adjacent to other overlapping features, to avoid dissolving with them. In this case, you may need to do the export/dissolve/replace separately for each pair of overlapping features.