This is a very hard question to answer with certainty because we, living today, know how things turned out. We naturally have a bias to think that the way things turned out was inevitable or was, at the very least, highly likely. Even though I am aware of this potential bias, I still think that the breakdown of the multipolar international system was highly likely. This is true because of the fact that there were countries that wanted to upset the status quo and gain more power than the system allowed them.
A multipolar, balance of power type of international system can be very stable. Such a system works because the powers in the system work to make sure that no one country gains too much power. But this becomes more problematic if countries that are not major powers believe that they should be major powers. If these countries can gain allies (from inside or outside the current system) they can disrupt the system as they try to gain power. This is what happened in the time period that you ask about in this question.
During the time between WWI and WWII, three countries that were not really powerful wanted to gain power. These were Germany, Japan, and Italy. Germany had been a major power before WWI, but it lost its power in that war. It wanted to regain power. Japan and Italy had not been accorded major status before the war and they were not seen as major powers after the war. They did not like this situation and wanted to increase their standing in the world. These three countries were able to join forces and disrupt the status quo, causing the international system to break down. This is, in my view, a highly likely scenario when there are outside powers that aspire to gain more power in the international system.