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I was thinking about a TL were the death of Lord Elgin (captured and tortured along with Parkes and Loch, shortly followed by his death while still a prisoner) causes the war to expand.
I am thinking about the potential ramifications:
Britain and France seeking territorial concessions and potentially interfering in the governance of China (I cannot stomach the phrase "regime change") in order to extort reparations and guarantee access to trade.
The potential survival, at least in the short term, of the Taiping government as the Imperial forces are redirected.
The Ever Victorious Army (whether under Ward, Burgevine, Gordon or perhaps Graham who was offered command) is still raised and taken into British pay but against the Imperials instead.
I am looking at either a potential scramble for China in the 1860s and 1870s (with Britain, France and Russia as the main players) or a Chinese Raj (but I cannot see Russia and France standing for this without substantial territorial concessions so we get back to the scramble scenario).