Hmm... China, either under the Manchu Dynasty or a new one akin to the Meiji Restoration, opens up to Western influence while Japan remains isolationist in the mid to late 19th century. China begins throwing its weight around and looking to exert its influence over historical territories and all of East Asia; Japan catches on later than OTL (1880s maybe) and overthrows the Shogunate and reestablishes the Empire. They modernize close to OTL, taking technologies/ideas from Western nations; in the end, though, Russia maintains the closest relations with Japan due to their common enemy in China and a Russo-Japanese Alliance is soon signed. War breaks out in the Far East at some point (in conjunction with a European war). Britain has maintained a close relationship with China but has a full plate with Europe and doesn't enter the Asian theatre, though they supply the Chinese. Russia breaks down into Red revolution and Civil War during the war but China has still been inflicted with heavy losses and Japan continues the struggle. China eventually breaks down into revolution as well and, by this time, the Bolsheviks have gained the upper hand in Russia. Japan fears for the spread of Communism into China and quickly ends the war, taking southern Korea and Formosa and mediating the cessation of East Turkestan to the newly formed Soviet Union. Japan installs a Nationalist government in Peking (lead by someone more capable than Chiang Kai-Shek) and tries to exert their influence over the European Asian colonies as the new master of Asia, but manages to only destabilize them further in an interwar period and breaks into constant small wars with Chinese forces. That's as far as I'll go there...
North America? The USA is cut off from expansion into the Pacific by the British-supported Kingdom of Hawaii in Britain's attempt to encircle the pro-Russian Japan. This difference manifests in the Spanish-American War that gains them Cuba and Puerto Rico and the Colombian War that gains all of Panama for the USA to create a canal, both within a short while and at the whim of the pro-Imperialists and robber barons looking for further economic expansion. This creates far more labor unrest and the blatant entry of the USA early into the European war against Britain and its allies via a pro-business President. American casualties mount and insurrections grow in their Latin American possessions, which are crushed ruthlessly and 'internment' camps, which are really concentration camps, are set up. Like Russia, the USA breaks into Red revolution and Britain quickly makes peace with the American government on the hopes of halting its spread, ceding most of Canada. The Communists gain the upper hand, however, and the American government is finally forced to flee to California where Britain supplies them via Hawaii and Mexico. A British-supplied Mexican invasion regains Mexico a portion of the Southwest before a treaty is signed in which the territorial adjustments, as well as the existence of the USSA and Republic of California, are recognized.
Good enough?