Regardless of whether they are SOEs or private enterprises, the state could have circulated reminders to uphold to high standards and conform to local laws. As for the SOEs, make it a standing policy of not tolerating briberies.
Other than that, leave them to subject to local justices.
Don't just do nothing.
Reminders yes. And yes with SOEs, there is already progress being made here.
But China cannot force private businesses on how to behave outside the country.
Chinese bussinesmen are very cunning and wont hesitate to take advantage of whatever loophole other countries have when operating there.
Xi cannot monitor every business 24/7.
If countries want Chinese companies to follow their laws then its up to them. Maybe they are willing to allow Chinese police and judges to come in their countries to enforce Chinese laws
/s
But then the locals would be screaming "China is colonising us! China will assimilate us"...
So how exactly do you think that China can enforce good behaviour thousands of km away from it?