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In the "Muslims are Stupid Because of Inbreeding" Chat thread, there's a chart depicting the genealogy of Charles II of Spain, he of the many genetic defects.
So are there any opportunities to get some new blood in there? I read that one reason the Hapsburgs got inbred was the Reformation reducing the number of eligible partners by virtue of reducing the number of Catholic nobles. Maintaining the Spanish-Austrian "Family Pact" was also important, although one wonders why they needed *so many* dynastic marriages, considering how closely they were related anyway.
Phillip II and Mary Tudor having a son and the son being overthrown in England after "Bloody Mary" dies might work without radically altering the timeline *too* much.