Presume the world went as normal, except Britain and Japan kept their alliance from WW1.
Just before ww2 begins expansionist glory hunters get into power in Britain who only care about their own nation
Nazi Germany fights France and the USSR (with US but not British support) on the continent. Japan isn't officially allied with the Nazis so there are two separate wars. Axis, Cominterm, Allies (USA +France), and team island.
Britain and Japan secretly arrange a plan to carve up Asia (Japan gets sino Asia, so China, Korea, North Vietnam, plus the event of a war with USSR the Pacific Coast), Britain gets Dutch east indies, Siam and Tibet. They split the Philippines?
They arrange to keep this secret from the USA so they give no aid to Japan until the date of pearl harbour.
Assuming this, would the empire conduct its own surprise offensive? Where would it do this?
What would the USA reaction be? Would the USSR fall because its cut off from USA (if island nation are neutral in USSR/Nazi conflict)?
How long would it take for the USA to build up to defeat the islands? Would they lose motivation?
How about Canada and the Caribbean?