How do I temporarily reduce the number of object vertices to be able to perform solids operations?

When working with a complex 3D object, too many vertices can generate error messages stating that the Geometry of the object makes Subtract Solids, Add Solids, Intersect Solids etc., impossible. One way of working around this is to split the object into two parts using the Split By Line tool/mode. After a split, each of the two (or more) components of the larger object contains fewer vertices. When an operation such as Subtract Solids, Add Solids, etc., is attempted, it is much more likely to succeed at this point. After the various operations have been performed, use the Add Solids command to recreate a single object again.