As with many practice issues, the answer depends on the state. Some states have "generic" PE licensing, others have "discipline-specific" licensing
One state (California) has a confusing combination of the two. In California, a PE in EE could *not* legally do ME or CE work (unless such work was somehow "incidental" to the practice of EE). And conversely, a PE in ME or CE could *not* legally do EE work (unless it was somehow incidental to their ME or CE practice).
However, an EE *could* legally do ChemE work, because ChemE is regulated differently (anyone can legally practice ChemE in California; the PE license only grants you a nice title). But a ChemE could *not* legally do EE work.