> At what point do their aggressions spill over into a larger conflict?
When perceived benefits outweigh costs. The US's multiple invasions of, and coup plots against, other countries didn't 'spill over into a larger conflict' because the US's power & ruthlessness have been well-understood by the world. The costs of resisting US militaristic aggression have just been too high. The same has applied to Russia, and perhaps will in China's case if it makes good on its threats (though it would have to fight on multiple fronts for decades to even approach US levels of aggression).
When perceived benefits outweigh costs. The US's multiple invasions of, and coup plots against, other countries didn't 'spill over into a larger conflict' because the US's power & ruthlessness have been well-understood by the world. The costs of resisting US militaristic aggression have just been too high. The same has applied to Russia, and perhaps will in China's case if it makes good on its threats (though it would have to fight on multiple fronts for decades to even approach US levels of aggression).