According to one Robert Pachmann, Crown Prince Rudolf of Austria (the suicidal son of Franz Josef and Elisabeth of Bavaria) was his father by a clandestine marriage to the tubercular Maria Antonietta Leopoldina of Habsburg-Tuscany (she was refused as a wife for him as unsuitable - due to her health - by his father). He lobbied long and hard to be acknowledged as the son of Rudolf (whether he hoped of inheriting the Austrian empire IDK). Now Pachmann, in all likelihood, was a cook (or perhaps he really was Rudolf's bastard, the Austrian courts of the 60s certainly thought so), but it got me thinking:
Pachmann a.k.a. Archduke Karl Rudolf Salvator was born on March 7 1883, his "mother" conveniently dying that same year, while his "father" married Princess Stéphanie of Belgium in 1881, although Pachmann claimed a wedding date of January 1 1880 for Rudolf and his Austrian cousin, meaning that Rudolf married bigamously!
Now, what I'm wondering is, what if the emperor had agreed to the marriage between his son and his Tuscan cousin? He could clearly see the girl is not long for this world, and in secret he can make overtures to various houses for a suitable bride, and then when Rudolf is widowered in 1883, he can marry another princess (if he was 'in love' with Antonietta, then his father can insist by saying the dynasty's future depends on it (although OTL FJ refused to sanction a divorce between Rudolf and Stéphanie after it became clear that they couldn't have more children, despite both parties being willing to divorce), so IDK).
Plus, if Pachmann really was Rudolf and Antonietta's son, at least the dynasty is secure - for the moment, at least.