Yes, you can extend your stay in Australia on a visitor or work visa. Still, it generally requires applying for a new visa, especially for visitor visas like the ETA (601) and eVisitor (651). To extend your stay in the country with these visas, you can apply for a new Subclass 600 (Visitor Visa), a Working Holiday Visa (if eligible), or a different substantive visa like a student or work visa, depending on your eligibility. You must, however, have sufficient proof of funds, meet the respective eligibility criteria, and must not have a 'No Further Stay' (Condition 8503) on your existing visa.