Could a liberal democratic China co-exist with the United States in a revamped Liberal International Order?

Is there any reason that a liberal and democratic China could not co-exist and even co-lead a revamped liberal international order in partnership with the United States? Perhaps the more ambitious aims of the order could be trimmed away like excess fat, leaving the core security, trade, and public goods functions. Why couldn't China and the US eventually cooperate in providing public goods such as securing the oceans and being the global policemen together? (Though perhaps the global nightwatchman function would be reserved for only the most existential cases.) Within the framework of the order, they could compete economically as other nations do in the order.

Or is the order just a patina for a raw US desire for pre-emminence, a desire that China now shares? And thus their goals are incompatible.

Here's a fascinating article by American affairs journal that compares the current China-USA situation to USA-Edwardian England instead of Cold War Russia-USA

The point of the article is to point out that despite being a "communist" country, modern China is far more of a State Capitalist country, and that Cold War analogies could be less accurate than England-USA competition analogies. (The article is also self-aware enough to point out flaws of its England-USA analogy too)

England and USA exist buddy buddy right now, despite USA having essentially usurped the British Empire at the start of the 20th century. And England is a perfectly good place to live, 100 years later