As mentioned in the title, how much expansion can imperial Japan gain without going to war with the USA? In other words, what level of Japanese expansion would America be willing to tolerate, viewing war as not worth the trouble especially with the Nazis in Europe. Also, will attacking British and French colonies be a deal breaker?
Japan was already stalemated in China. China was poised in late 1941 to start receiving a large amount of US Lend Lease plus additional support (such as the AVG). If the pipeline of supplies is not interrupted, China could probably begin to conduct limited offensives against isolated Japanese garrisons - most likely the port of Canton. By 1945, it'd likely even possible for large scale offensives to happen.
If Japan avoided an attack on the US but attacked the British or Dutch, the US would complete any last remaining checks on its economic warfare against Japan, put it's entire military on alert (preventing any possible future strategic surprise attacks), and explore ways it can additionally help the British Empire short of war in both the Pacific and Atlantic.
The US Navy and air bases in the Philippines essentially act as a Fleet-in-Being the Japanese can't ignore. They have to keep certain forces ready in case the US attacks.
The US will likely blatantly send supply ships to Australia - daring Japan to attack them and start a war.
There could very well be a US volunteer mission to send troops to Australia in order to defend that country in case of Japanese attack. They'd be recruited, trained, and equipped in USA and sent to Australia, and be able to quickly "nationalize" under US colors should the US enter the war.
Britain could also very well turn over various Pacific Islands over to the US through various legal means in order to keep them out of Japanese hands and extend the US threat into the Pacific. They could be outright purchases, base leases, occupations, or whatever. FDR could be very creative in accomplishing whatever he needed.
In the meantime, the US continues to fortify its Pacific islands defenses and build the ships authorized in the Two Ocean Navy Act. MacArthur foolishly did not believe Japan would attack prior to April 1942 by which time he'd have made the Philippines much more ready to handle a Japanese attack. ITTL, the gamble pays off.
Unbeknownst to the Japanese, the US is also going to be able to provide the British with a lot of intelligence thanks to breaking the Japanese naval codes.
Japan isn't going to be in a good strategic position, and it can't get much more than what it could occupy IOTL because of the need to keep a reserve against the US Fleet-in-Being except that all the US losses don't happen so there is a big potential danger in the Philippines.
It could neutralize US support for China by invading Burma as IOTL, but there are more roundabout ways for the US to deliver aide to China (say land route or air supply from western India to Hotan and going long land route to Chungking) and all material would end up going to China instead of being diverted to the US air force there.
And of course, Japan risks the US entering the war at a time of their choosing. The US could enter the war in 1943 with the same navy it had IOTL except still have Guam, Wake Island, and the Philippines - meaning it's a year ahead of the gains it made IOTL.