So I thought up a possible scenario regarding Austria-Hungary.
An infamous AH cliche is that had FF lived to become emperor, he would've "saved" the country by doing a short-lived "civil war" against Hungary, and prevented/delayed WWI.
What I came up with after reading several threads about him and Austria-Hungary is that since he was autocratic, deeply against Hungarians and conservative, he might not be a good way to save the empire.
Therefore my POD is that, upon marrying his future wife Sophie, the rest of the Habsburgs declare that not only are their children considered illegitimate to the throne as OTL, but FF himself becomes.. not exactly "illegitimate" but his marriage in this POD equals he is bypassed in favour of Karl (the same Karl that succeded FJ OTL)
So after that, you just need FJ to die in 1916 as OTL or you can kill him off earlier as in 1908 of pneumonia or in 1914 of a stroke. (both of which nearly killed him OTL)
And finally, the reason why I'd want Karl to take the throne even with FF still around is because he's been referred to as FF "lite". In that, he was everything FF is said to have been, but not to the same extent. and seen as a more "sane" individual to deal with the Ausgleich once that becomes a thing in 1917.
Also, how does Karl's reign go now that he's not succeeding the throne to a country at war?
And of course, the million dollar question, Can Austria-Hungary survive in this scenario with him as emperor?