TG fly SYD-MEL but not MEL-SYD - I doubt they can be of much help either as I don't think they have local traffic rights (like UA). I am pretty sure UA wouldn't permit a stop per Al B's comments.
Last year I did fly MEL-SYD(UA)-KUL(OS) but that was an online connection. Even still UA at check-in at MEL gave me a hard time as it wasn't a UA-UA connection. Eventually they let it pass as the computer printed out the bagtag and I think they just didn't want to cause trouble over it.
Back in the glory days of the Star farex ex-Australia you actually could fly to an Australian gateway city and stop there. I think the rule was "one stopover allowed in Australian gateway city" - now of course MEL is a gateway city, but if you were creative with your routing (guess who puts their hand up!) you could get in another domestic oz stopover for nothing. One example I did in 2000 was MEL-PER (stop) on AN and connected to TG flying to BKK via HKT.
Of course now that AN is resting in peace this isn't really an option these days, but that was a great rule while it lasted.
Ah, memories...
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RichardMEL, UA 1K
A Star Alliance Member.