the best addition to the Axis would be Finland, not sure what scenario would make them join (?) maybe German support during the Winter War or maybe Finns decide Leningrad needs to be taken to insure their security.
Given as Finnish participation in the war against the USSR was IOTL grounded on realism - Finnish resources only really warranted the kind of advance and occupation that was achieved IOTL, and the Finnish political and military leadership were careful not to burn all the bridges to the Allies to prepare for the possible eventuality of Germany not winning, I'd say the only way to get Finland to "fully commit" to Barbarossa and German (as opposed to Finnish) war aims (as is often asked on this forum) would be to have such people leading Finland that are for one reason or another ready to throw all caution and sanity out of the window in 1940.
One way to achieve this might be to kill off Mannerheim and some of the leading non-pro-German and non-radical politicians, like Ryti or Paasikivi, in the 30s (maybe it is a lucky Soviet bombing during the Winter War) and tweak the timeline so that the people that rise to positions of leadership are Germanophiles and Greater Finland enthusiasts to boot. Rash personalities would help, too.
This is a very tenuous way to do it, though. For a better effect we could pull off changes in the interwar, even from 1918, that would make Finland a Fascist or at least right wing authoritarian state. Such a Finland, if it survives the Winter War (which I doubt), would be much more amenable to go to greater lengths to support the Nazis come 1941 than the stolid bourgeois republic the nation had IOTL become by the late 30s. But then of course we would have to worry about the butterflies the political changes in Finland would have caused earlier, locally and abroad.
Anyway, we wouldn't want to count on a Fascist/authoritarian Finland being a lot more useful ally to Germany in comparison to OTL Finland. Given how politically divided such a Finland would be, the leading right wing elites would have to keep down the left heavy-handedly and internal problems would take away resources this Finland could wield in *WWII - it is a possibility this Finland might even field a smaller military and one with parts more likely to disobey orders or to mutiny than the OTL Finnish armed forces.