If history is to be believed the combo of Vincenzo I Gonzaga, duke of Mantova's spending, the plague, and the War of the Mantovan Succession was the death knell for the state of Mantova. An interesting side effect was Giulio Mazzarino ending up in France. Now there are numerous ways the war might not've happened:
1. Francesco IV survives his attack of smallpox in 1612 and fathers a surviving son.
2. Francesco's infant son Ludovico survives whatever killed him.
3. Ferdinando acknowledges his son by Camilla Faà as his heir and said boy survives
4. Ferdinando has (a) child/ren by Caterina de Medici
5. Vincenzo II marries again after the annulment of his first marriage.
What do you guys think?
Well, I can't find what killed Ludovico, so if we assume that it was your normal childhood illnesses that were usually fatal in those days, then if Francesco IV survives, Margarita of Savoy is gonna probably keep punching out kids (like her sisters) and one of them will most likely be a boy.
Ferdinando acknowledging his son is a little more difficult. His family was dead set against the match, not sure if this was as a result of him being the duke or not, though. He seemed to stand fast against them at first, but eventually caved and had an annulment granted. That said, what might be interesting, is if the annulment (as some others have done) were to render the marriage null and void, but the issue still legitimate (see Monaco's Grimaldis), or to where a secondary decree declares the little boy legitimate (like with the Beauforts). However, the little boy would stand behind any issue lawfully begotten with Caterina de Medici, which is gonna make him a target for the traditional weapon of the Medici: poison. And indeed, when Giovanni died OTL, there was a strong suspicion of poison, although it never got further than that, since AFAIK it was the plague that carried him off.
As to the Vincenzo possibility, IDK enough about him. Perhaps if he's married to another wife from the get-go (his OTL wife was a widow, 10 years older than him, and I'm not sure why they even married to begin with, she wasn't an heiress AFAIK).
Of all these possibilities, I like the idea of Giovanni Teodoro Gonzaga (son of Camilla) succeeding as duke. Obviously a deal will have to be made with whomever (the Pope, the Emperor, other Gonzaga branches) but considering the d'Estes had succeeded like that, Alessandro de Medici
was an unlegitimized bastard and the Farnese were descended in bastard lines from the pope and the emperor, I don't think it'll ruffle too many feathers. Most of Europe's got bigger fish to fry than a duchy in northern Italy. Hell, when Austria seized it OTL a century later, no one even raised a point of there being legitimate heirs to it (the Gonzaga of Guastalla).