During the Cold War the United States followed the Containment policy to isolate, limit, bind, and strangle the Soviet Union. They even made a deal with China to do that. This policy played an important role in the collapse of the Soviet Union.

In a multipolar world this does not work.
For now we have three powers leading this emerging world order: USA, China, Russia. If one tries to Contain another, then the other two just plays this out using each other. For the Containment to work two powers have to decide to isolate the third.
If the enmity between two powers gets to strong, that is a golden opportunity for the third to corner one of them by offering a helping hand to the other. Not one of them can afford to this to happen.
All three powers are rivals and potential allies for each other.
The new world order won't be a cold war, it will be a balancing act between the three until a fourth or a fifth emerges, then we'll see, they will continuously approach and push away each other, they will try outbid each other for the favor of each other. It will be a difficult courtship.

However this will be influenced by their power ranking. The the weaker powers see the most powerful more of a danger than each other. So whoever leads (now the US) will be on less favorable terms with the other two than they are.