[LeonB]

You wouldn’t need to get “approved” to do so…

You’d go back to your regular non-specialist doctor, your GP, and ask for a new referral to a specialist, explain that you want a different one, and why… the GP would give you the referral.

You might end up seeing a “private” specialist - Medicare would pay some money toward it, but the gap, the extra bit, you pay yourself (or if you have medical insurance, your insurer pays it). The insurer doesn’t waste time checking before hand whether you are or are not “approved” - and the “gap” for seeing a specialist might be $200, not much more than that.

If you don’t want to pay any money, then you wait longer for a “public” specialist to be available. It might be the same actual specialist btw, as the public hospitals are good hospitals.