Not to discourage any further discussion, as there is always more to be said, but you may be interested in the answers to these previous questions: What was the basis for Japan's alliance with Germany during WWII?; What did Hitler/Nazis think of Asians? (by u/ParkSungJun); What were the nazi plans with japan if they had won the war? (by u/mr_darwins_tortoise); What was Hitler's endgame? (by u/Georgy_K_Zhukov).

Although the linked answers above can go into far more detail than I can, the TL:DR is that neither Nazi Germany or Imperial Japan had plans for “World Domination”, but wanted to control their own spheres of influence (Europe and South-east Asia respectively). Therefore any collaboration, or potential future conflict, between the two would likely have been minor or non- existent. Overall this is a difficult question to answer, as it is the role of historians to study what has happened in the past, not what could have happened.

It is also worth noting that, for the Nazi’s at least, very little is known about their post-war plans, the Generalplan Ost (GPO), as most copies of the plan were destroyed and had to subsequently be pieced together from various sources. Furthermore, the Nazis only ever implemented small parts of the plan, and constantly deviated from their original intentions in response to changing conditions of the war. So there is no way to tell if the GPO would ever have been fully implemented if given the chance. u/commiespaceinvader offers a good summary of GPO in their answer to this question: Why is the Generalplan Ost considered different from the Holocaust?