Besides the Kallipolic Confederation and China, there were numerous other nations in the Plato Succeeds timeline. Some eventually joined either superpower, some adopted either's ideology but stayed independent and others maintained their independence from both powers completely. This article contains several notable examples.
Ancient world- 30th century BC to 500Some Northern European tribes adopted aspects of the Republic but were not members of the Confederation until the Roman conquests. These include the Iceni, Silurians, Arverni and Belgae. However, the Picts, Scandinavians and Irish remain untouched until the spread of Christianity.
Rome stubbornly resisted the Confederation until it was conquered by Epirus and became the Roman Kallipolis.
Carthage was destroyed in 146 BC. It had been a major land and naval power to Rome before that cities conquest and still launched attacks on it after. In this war, its ally Syracuse was taken and the scientist Archimedes captured alive, providing a major technological boon. Carthage itself was exterminated in a controversial assault which resulted in a massacre that shocked much of the Platonic world.
Any nation in the Americas or much of Oceania would be independent due to lack of contact with either.
The south of India and sub-Saharan Africa remained independent, as was Japan.
In 224-256, the Sassanid Persian Empire was established in the remnants of the Parthian Kallipolis (it had weakened following a Palmyran assault on its capital Ctesiphon). It wanted to revert time back to the former Achaemanid Empire and viewed all time between then and their present time as irrelevant or even non-existent. However they were not able to withstand the attacks of nearby states and internal dissent. The peasants had been slightly relieved when the Guardian/Civilian distinction was done away with, but then found themselves dragged from their homes and farms, whatever they were doing and forced to take part in wars they didn't want to fight. As such, in this timeline the Sassanids only reigned for 32 years. The replacement Persian Kallipolis did not return the region to prominence until the Age of Division, where it received aid to help repel the Chinese advance.
The Middle Ages 500-1500
Japan- this chain of islands fiercely staved off all attempts to violate the land of cherry blossom. No new ideologies are to be introduced other than Confucianism and even that remains a minority compared to Shinto and Buddhism. Japan remained untouched even after China starts to set up colonies in North America in the 1220's. Japan even had the weather on its side- the Chinese-Mongol fleet of Kublai Khan was destroyed by a kamikaze (divine wind).
The Aztec Empire and other Mesoamerican nations (major ones being the Inca and Maya- see more about the latter below) until either the 1220's or 1492 based on whether encountered by the Chinese or Confederates. The North American nations around what we call California were quickly converted to Confucianism, but many stayed independent.
The Aborigines and Maori's were left untouched until 1400, when both Confederate and Chinese fleets encountered the respective nations. Converting them was extremely difficult.
Lithuania remained independent until conquered in the 1200's by the Teutonic Order. Northern Eurasia was a frequent target for China, which conquered it all the way to Siberia.
The Bantu and other southern African states were left untouched. Sub-Saharan Africa was expanded into, but some nations were either inaccessible or resisted conversion, such as the Berber's or Tuareg.
The Age of Division 1500-1700
In this era the Confederation is nearly torn apart by larger internal conflict than usual, which the Chinese and other "rogue" nations take advantage of. However the Chinese themselves later get affected and are taken over by the tribes of Manchuria in 1644.
Border Princes: the Chinese Empire managed to go through most of Russia at the start of this century. However Poland and the Teutonic Order were able to hold them back with help from Norsca and the Persian Kallipolis. The area between Kallipolic control and China was left alone, with the people living there banding around powerful warlords to keep themselves safe. This could be considered the most dangerous area in the world as both China and the Teutonic Order as well as the Princes themselves could at any time raid anywhere within. Of the Princes, 70% were male, with the 30% of females also known as Princes. Not that this made much difference to their victims. The Border Princes lands were eventually restored to Confederation control when the Age of Division ended.
Japan was still independent. Although it had acquired some up to date technology, in 1633 Shogun Tokugawa Iemitsu isolated Japan from the rest of the world. However the Dutch were still allowed to send in one ship a year to Nagasaki, then leave immediately.
South Africa was not conquered or assimilated by any superpower,
Maya: many tribes were left untouched by both European and Chinese adventurers, untouched meaning their cities weren't plundered and the inhabitants made subservient to their new masters. The Mayan people knew that the "blow-ins" (a term adopted from some native South Americans) were deep down just as mortal and vulnerable as they were and only dominated because of their advanced technology. Therefore, the logical course of action would be to get some of this technology. Not only would this deny the outsiders their use and allow the Maya to use them against their former owners, it would allow them to reverse engineer and discover how they worked. The Maya also set out to study the manufacturing methods and machinery. With these, the independent Maya worked to liberate the others of their race and all Mesoamericans. Using the chaos of the Chinese-Confederation colony war as a cover, they liberated much of Central and South America and fiercely defended their reclaimed territory from any incursion. They were also able to develop their own space program, which verified that humans had walked on the moon. The Maya ordered the abandonment human sacrifice, it simply wasn't needed after all. Most of their technology was of Confederate origin, sometimes deliberately smuggled to them.
See also Reform Union (Plato Succeeds).
The downfall of Confucianism 1700-1842
While the European Kallipoli were fighting each other, the rest were preparing to finish of the ancient enemy China. At the same time both superpowers were sending colonists to new lands.
The Iroquois: 5 later 6 tribes all over North America. The Iroquois were encounter first by the Confederation so were a key target for conversion.
Maori and Aborigines were safe from imperialism until the 1720's. As both superpowers were at war with themselves and each other, uncolonised land stayed free, but the islands of Australia, Tasmania and New Zealand did not escape notice. At the very least, the land can be used to dump criminals.
Mthethwa Paramountcy and the Zulu Kingdom: these south African nations were the last to remain free before the Confederation moved in to deny the Chinese the chance to do so. These people were formidable enemies no matter how they were armed and are often praised as worthy foes.