A TL stemming from this-
Given the Jameson Raid occurred in 1896, and the alteration is Kruger is more demanding and the British do not completely disavow the raid, the Boer War begins in earnest in 1897, with Britain as the aggressor in the eyes of world opinion, and being not terribly successful militarily at first.
In 1897 in Europe and the United States, the Boers are more popular than the British.
But the US will be circumspect, especially as the McKinley administrations wants to be circumspect and the Venezuela crisis is over.
The European powers, while being anti-British in their hearts, are going to be wary of actually fighting Britain or provoking her to war.
The Russians, Germans and French main agenda will to act as they did in OTL, boosting their expansion/exploration in other areas and in particular, wringing concessions (Qingdao, Port Arthur, Guangzhouan) from China.
The British under Salisbury or Roseberry are going to be straining to make overtures to the French and Russians that neither will embrace.
Britain will have to think carefully if the present time is a good one to launch a campaign to crush the Mahdi. IF they do campaign in Sudan in 1898, and Marchand wants to march through from Central Africa to eastern Abyssinia, they better let Marchand pass and the French have their way. Because a Boer War and a Fashoda war at the same time are a very bad idea. A hot Franco-British conflict in Africa has a high probability of bringing Russia and possibly even Germany and Netherlands in on France's side due to outrage over the Boer War, Britain's demonstrated ambition and arrogance (shown by their hardline against the French in Africa) and the availability of an ally with some power projection onto the African continent and global stage to bear the brunt of British wrath.
(In this extreme variant of the continental coalition Britain will still be able to win in South Africa and the overseas world at least beyond Suez and Gibraltar, if not within the Mediterranean itself. If it's absolutely war to the extreme, Britain might lose in Persia, north China and Korea, while winning in all of Africa, Indochina, Indonesia and Oceania)
So, the British will probably put off the whole Sudan campaign and avoid the nightmare continental coalition altogether.
The British will turn the tide in South Africa and eventually win. They'll do enough to keep out of war with France or Russia. Out of their continental critics, the British will be most bitter against the Germans, because they'll blame them for encouraging Boer intransigence leading to war.
...but actually attacking Germany or its empire is far too risky a move for the British government to make, so there is no British declaration of war on anybody besides the two Boer republics, which do fight together the whole time. The British eventually secure a Boer surrender in 1899. With that war concluded, the British make an alliance with the Japanese, and can feel free to launch the Sudan campaign and be assertive against France there without risking a global war.
As far as further knock-ons are concerned, perhaps the Japanese attack Russia in 1902? If they do, perhaps the Austrians intervene in reaction to the regicide of the Obrenoviches in Serbia in 1903.
Thoughts?