Yes, I think you can increase your mileage a little. There are far more expert tweakers than I (and I don't mean that in the pejorative meth-addled sense ) here in the OW forum. It would help to know how set you are on particular destinations, and whether you'd be up to doing a couple side trips.

jnb-syd-per-mel-akl-hkg-akl-scl-ccs-scl-gru-jfk-bgi-jfk-lax-lhr-jnb

is 59876. But, you'd have to take the train from CPT-JNB (which I'd love to do someday), and do the 400 mile trip to ADL by ground or extra ticket, and finally, it's about 220 GRU-GIG. Caveats include the fact that I did not proof this on the oneworld site, and I hear the akl-scl is a bear to book.

Also, this is a *one6. If you leave out Asia, you'd save about 1300 USD on a D fare, 2000 on an A fare. And you'd have two segments to spend in NA or Europe.

I'm assuming, perhaps erroneously, that you aren't considering L? Nothing wrong with L but you're interested in miles. Many carriers give 0 miles on that fare, and only two, I think, give full credit. Wish there were a way to do two DONE3s and hit all six continents, but I don't think it's possible. To really maximize miles per dollar spent, I think the consensus is that *ONE3s are best. From SA, where you MUST have at least 4 continents, two DONE4s cost $4152 more than a DONE6. So 16 extra segments will cost about $260 each. This may be totally irrelevant to you--I don't know your time constraints, for example, but food for thought.