Are there any avenues for an E3 Visa holder to become a permanent US resident?

Although the E-3 is not considered a dual intent visa, it is one of those visas which is in the gray area between that and requiring no intent to immigrate. If your employer is interested in sponsoring you for the green card, I suggest that you should remain in the country without leaving during the period of processing.  That would perhaps be safest rather than risking a problem with either applying for another visa or re-entering the country.  Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.