From this answer, privileges of single-engine and multi-engine are separated. A pilot who obtained his PPL on a single-engine and his CPL on a multi-engine is not permitted to exercise his commercial privilege on a single-engine airplane. To do so, he must past another CPL exam on a single-engine plane.
Why is this do? I see no reason why a pilot who can operate a multi-engine airplane safely is incapable of doing the same in a single-engine. Training in a multi-engine would include an all-engine-failure scenario, which would be similar in single-engine.