Which navies conducted joint counter-piracy operations?

Were there joint counter-piracy operations with forces outside the British Commonwealth?

Yes. Chinese forces joined regularly, Americans participated on several occasions, and some operations even involved Japanese cooperation.

The answer separates routine cooperation from occasional participation. Chinese forces were regularly included so that operations could be described and conducted as joint action. American units sometimes joined British operations, and British ships also worked alongside Americans. There were even occasions of cooperation with Japanese forces. Counter-piracy thus created practical coalitions among powers whose wider political interests did not always align.