Well, thing is, if it's the AAA and the Technocracy, the primary theater would be in Africa in general, compounded by naval and air actions in the far east.
It's likely that the AAA would try not to draw the Turin Pact into the war. For one, every member of the Alliance is subsaharan, and while the Turin Pact does have a large presence in Africa, it's in North Africa. It wouldn't really add strategically to their depth.
So, it's likely that it'd be the Commonwealth vs the AAA & the Technocracy, with other alliances eventually joining in. Let's look at the primary fronts that might face assault.
Nigeria would face a two-front assault, as West Africa would press from the west and Umbangi would provide some pressure to the East. As West Africa can't press north (again, neither Morocco, which probably leans sliiiightly to either the LAR or the Turin Pact, nor Ghana/the Sahara Republic, provide them depth), and conquering Equatorial Guinea and Liberia don't really add much of a strategic advantage (besides ticking off the LAR in the latter case), so West Africa would be forced to invade into Nigeria. Umbangi's second front wouldn't add
much to the assault, as they have other priorities, but attacking and knocking out Nigeria would be a major victory for them, and would open up the rest of Africa for West Africa to operate through (as the Commonwealth will have control of the sea).
Simultaneously, Umbangi and Abyssinia/Aksum will invade Gordonia, in an attempt to link up with each other as well as creating another connection with Congo. As Gordonia is so remote from the major sources of Commonwealth power, it would be best to strike first and eliminate them from contention before East Africa can reinforce. Then, the AAA can assist in holding off East African counterattacks.
Angola and Mozambique will likely try to bridge the gap in Zambezi, creating an AAA Pink Map in the south. It would be their responsibility to hold off South African reprisals while the stronger members in the North consolidate their gains. If West Africa links up with Abyssinia et al, they can then attempt to provide a front against East Africa and march south into Katanga as well. I'm assuming here that they are avoiding the I.C.R., as I believe that is AES aligned. The key concern for the AAA here is to NOT bring in as many alternate alliances as possible.
In the ideal scenario for them, they manage to overrun enough of Nigeria so West Africa can field further assaults elsewhere in the continent and the AAA spreads to every country that they invade, with puppet regimes being set up in a balkanized Nigeria and East Africa. Then, after a period of temporary peace, perhaps 10-15 years in the future, they'd launch another assault to take the German aligned states and, in the end, create a unified alliance, with the only holdout being South Africa. Minor states such as Equatorial Guinea, Liberia, Puntland, Somalia, etc can be taken later on once major opponents are defeated.
...Now I'm reminded of Napoleon IV's plans for his world conquest. First step: Take over minor states, establish puppet regimes, rebuild. Next step, a decade or two later, take over anything nearby as you cannot effectively be fought and neuter opposition.
For the Commonwealth, the key here is Nigeria and East Africa. As long as those two nations manage to hold, any sort of AAA advance will be pretty much stalled. South Africa, I feel, can easily take Angola and Mozambique combined, especially if prepared. If that is the case, then South Africa can maintain the corridor to East Africa, force Angola/Mozambique into submission, and join the front in the North to liberate Gordonia (which I think would fall in any case).
And we're also assuming that the AES/Turin Pact/LAR don't intervene on any sort of level as well. If any other alliance joins the Commonwealth (as all of those alliances
are opposed to the Technocracy, and as a result the AAA), then the AAA's fortunes fall drastically, as new fronts are opened against them and their own military is forced to defend incursions. Economically, they are cut off from the largest trade partner (which I imagine is China), so the economy may devolve into a downward spiral.
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The Technocracy doesn't have the power projection to effectively intervene in Africa, but they can play havoc by diverting resources and terrorizing Madras/Malaya/Australia and the rest of British possessions. Burma is in dire straits as well, as the Chinese army likely will overwhelm any opposition unless, again, the defenders are well prepared for the assault.
Considering the threat that continued Technocratic expansion entails, it's likely that further expansion brings in the PTO and perhaps the CSAS as well. Russia will also join in against the Technocracy if there is
any chance that the Technocrats will lose. They will want to reclaim Manchuria.
The biggest wildcards would be India and Indonesia, though, and I'm not sure how they're aligned and if they'd even be interested in either side.
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On another note, update the old Alliance map to 2018. Hopefully everything is good, though many changes aren't shown. Biggest things I can think of is Umbangi and Angola now being AAA, Suriname joining the LAR, Netherlands leaving the AES. Of territorial changes, the only one that I think would be shown is Madras gaining the Andamans, the rest were changes in status while maintaining their alliances.