Hokay: I found the "Roma Eterna" setting in GURPS Alternate Earths rather contrived and unlikely, so I decided to cut them down to size.
(Background: in the GURPS setting, the Roman Empire did better than in our world, and when it did fall, it managed to reunite from an egypt-centered base - there was no rise of Islam or Christianity. The second Roman empire conquered all the way to India, and established colonies in the Americas, before crumbling in its turn: now, thanks to superior military tech (if no real science) the American Romans have returned and easily conquered everything from Portugal to India, and moreover are having no great difficulty running this huge ensemble. Can you say wank?)
The Hesperian Romans from across the sea had been initially welcomed by several of the successor states to the second empire: there was considerable popular support for the end of intercine warfare and the reestablishment of the Universal Empire. However, the honeymoon was generally short as the general _foreignness_ of the west Romans, with their barely comprehensible semi-Latin and disgusting spicy food and breathtaking arrogance began putting in place new administrative systems that gored all sorts of goats, and before long were extracting taxes to pay for wars against resistive Persians and Scandinavians and Indians.
In the end, the Long War with Taehan (which had very adeptly copied Hesperian Roman military tech and conquered half of the Serican lands before the Romans decided they were an actual serious threat) with it's expenses and levies of men proved the last straw, and touched off a series of rebellions that, given the Hesperian Roman's stubborn insistance in fighting the rebels and the Taehanese at the same time, ended with the Hesperians losing most of the conquests of the last century and making a peace with the Taehanese that left their core territories intact. An emperor was assassinated by his own troops, and things did not settle down for a while.
In the wake of the Roman withdrawal, the so-called War for the Imperial Crown broke out, as local kingdoms reestablished themselves and tried to grab as much as they could. In the later phases the Hesperian Romans took advantage of the mess to regain some of their losses, and the Gallic, Germanic, and Greek states joined forces to establish a peace (and smack down the Egyptians) and, more importantly, keep the Hesperians from coming back. The League of Roman Nations is _trying_ to create a sort of federal empire, with a capital in Italy: whether this will work in the long run remains uncertain.
(Italy, long fought over by Gallia, Aegytos, and the Greek Romans regained unity and pride as a unified province under Hesperian rule, and was actually rather unhappy to see them leave: it is the biggest supporter of the idea of a deeper, closer union, and dreams of being the leading nation in a unified Romanitas which doesn't include the chili-eaters).
Scandinavia was rarely part of the Imperial system of things, and Britain swam in and out of Roman rule over the centuries: the Alexandrian Empire, whose principal axis of expansion was east after the Persian empire was smashed by the Turkish Volkswanderung, only reestablished rule for a couple of centuries. As a result the nations of the North carried out their own colonization projects in the Hesperides, of which the League of the Western Landfall is the last survivor: too large, too cold and too warlike to be worth the trouble of conquering, it is an only occasionally annoying neighbor to the Hesperidean Empire.
The kingdoms of India, partly by land, and partly by sea, were mostly conquered or vassalized by the Alexandrian empire, but given their huge numbers and distance, were never really Romanized, and the Rajahs weren't particularly glad to have the Hesperideans show up and tell them to rejoice that they had returned to Restore Order. They would keep their own lower castes in line themselves, thank you very much! Roman military superiority and divide-and-conquer briefly re-unified India under Roman rule, but it was probably a doomed project even if the Long War had not intervened.
Currently, the Romans are working to crush the Huaracans, which they conquered as a bit of a consolation prize: devoutly religious people, the Huaracans are carrying out a resistance movement of Afghan ferociousness and determination from their mountains, to which the Romans are responding with overwhelming force: nearly a quarter of the population is already dead. Romans will not back down: there is a matter of face at stake, and the Huaracans will either submit or be exterminated.
The Taehanese are currently Breeding Prodigiously and taking advantage of Roman distractions in the Andes to do some colonizing overseas, particularly in Africa. This Has Been Noted in the Hesperides.
The world does not have as yet a genuine science, although cut-and-try engineering techniques have advanced considerably in Hesperian Rome and Taehan as a result of the long war. Technology in steam and transportation is perhaps mid-to-late 19th century, military tech in some fields almost 20th century (both poison gas and rockets are used in warfare), and telegraphs are widely used. The Taehanese invented the railroad, and have been building a network of rail to connect their territories: the Romans have begun to build rails of their own, their steam-powered road vehicles being crappy enough that rail transport shows some convincing benefits. Steamships are increasingly displacing sailing ships. Agricultural technique has benefitted from increased contact with the Sericans, and in the more developed areas of the Empire is now comparable to European 1700s production rather than 1500-odd, although steam tractors are still too expensive for the average peasant. Some lunatic has added the rocket-powered hot air balloon to the rocket-powered glider in the Bad Ideas category, and a Serican alchemist in one of the League of the Vermillion Bird states has come rather close to the idea of the fuel-air bomb...