What is the maximum period for which Australian visitor visa (e600) is granted?

For accuracy, the visa you describe is Visitor visa subclass 600 which allows stays for up to three, six or 12 months.

The Visitor e600 Visa Online Applications is the electronic tool through which eligible passport or travel document holders can apply.

Visitor visa (subclass 600) has five streams, and multiple factors are evaluated to determine visa duration.

With Visitor visa (subclass 600), length of time it is valid (and cost) would depend on the purpose of the visit(s), the validity period (expiration date) of the applicant’s passport, and for some, the nationality of the passport holder. For example, those in the Frequent Traveller stream, who must be Chinese passport holders, may be granted a visa valid for a period of up to 10 years. The long-validity, multiple-entry Visitor visa option for Singapore nationals can be valid for a period of up to six years.

Similarly if I apply for a e600 visa and select maximum length of stay = 3 months (in the application form) + request multiple entries, what would be the maximum period of validity granted on the visa (assuming the application is successful).

It would depend on the application; myriad factors are weighed and no set formula applied, although guidance and experience suggest what may be reasonable, realistic, and appropriate.

By comparison, other options allow for visits of up to 3 months (and cost less or nothing):

Electronic Travel Authority (subclass 601) for visit or business (not work) allows entry as many times as you want for up to a year. On each visit you can stay for up to three months.? It is valid for 12 months from the date of issuance, the expiry of your passport, or earlier if a current visa exists in the immigration system.

The similar eVisitor (subclass 651) for passport holders of certain countries and free, allows visitor or business visits purposes, again for up to three months at a time within a 12-month period.? It, too, is valid for 12 months from the date of issuance, the expiry of your passport, or earlier if a current visa exists in the immigration system.