Well, Germany trying to have influence in Brazil (or anywhere in America) is NOT a good idea. If you're Germany at that time, you don't want to do ANYTHING that MIGHT make the USA unhappy with you (if you can avoid it). Touching to American continent (which was seen by the USA as their big sphere of influence) is a no-no.
Also, having Portugal as a neutral can be useful. If there is ever important tension between ETL and Anglo-Americans, Portugal can help to mend fences, having some ties with Spain, Italy and Germany (Salazar supported Franco along with Mussolini and Wagner), while having an old alliance and ties with Britain.
If there are important tensions with Anglo-Americans, and an embargo for example, Portugal can also be used as a middleman to trade anywhere.
Also, if the Soviet Union is beaten, I expect Turkey to take influence over Azerbaijan, which will allow the Turks to reach control the Chechens, Ingushs and Daghestanis. Basically, Turkey would "protect" Caspian Sea Muslim peoples.
I expect Germany to "protect" Armenia and Georgia. Not least, because the Armenians might fight like mad for Stalin if they fear the Turks taking them over. Also, WWI plans included Georgia in German zone. Which makes sense, because Armenia and Georgia are on Black Sea, behind Ukraine and Circassia.
Even the Turks themselves might not want to "protect" Armenia and Georgia, christian countries, that will be more trouble to them than they're worth.
If Soviets fall, Persia will get back its independence and become a member of the Axis. Iraq (already member of the Axis) might use the occasion to take the Chott-el-Arab.
Central Asia might become a loose protectorate / vassal-ally to the Germans, allowing them to have Luftwaffe and Wehrmacht bases there, and threaten Russia at any moment, and to exploit the local resources (for a reasonable price). The Germans will never be able to directly and heavily control Central Asia like they can do in Ukraine or Caucasus, because there is the Urals and distance in between.
And of course, Japan will want to make Mongolia a protectorate (with Greater Mongolia), but with lighter control than in Manchuria (because logistics, again). Japan will also want to take over Vladivostok, and any resource-rich area in Eastern Siberia (either under direct control, or "Mongolian" control).
This Japan seem more reasonable than OTL. So, they may not try to have Kamtchatka, because if would make the US nervous and be unnecessary expense.
Germany herself, of course, will want influence over the Baltic countries, Byelorussia, Ukraine, Crimea, and likely Finland (including Eastern Karelia), Circassia, Armenia, Georgia, Central Asia and Persia as well. With heavy influence for Byelorussia, Ukraine and Baltics, and light for all other countries.
If vanquished Russia is allowed to have any military at all, there surely will be huge demilitarized zones in Russian territory, at all borders (including with Japanese Empire, Turkey and Central Asia).
Finally, I know that the Soviets have many disadvantages there compared to OTL. But they also have some advantages. Finland is invaded, which protects Leningrad, and Sweden won't join (at first at least). Soviet Union will likely not be surprised, but expecting an attack. Soviets will be more prepared, with fighting Finland longer (long enough to conquer it), and fighting Britain, Persia and Afghanistan. And the Soviets still have a huge industry, lots and lots of resources and manpower, and can retreat behind the Ural.
So, personnally, I don't presume that the Axis will simply win. There is a good chance of that, but no certainty.
