Cosimo III had some odd ideas about establishing cadet lines of the house of Medici (albeit, then, it was on its way out). I mean, take the plainest princess in Europe (Violante Beatrix of Bavaria), the second gayest prince in Europe (Gian Gastone) and a crazy horse-whispering duchess (Anne Marie Franziska of Saxe-Lauenburg) and I don't really think there was much hope for it - either in Lorraine in the Treaty of Nijmegen or in Bohemia twenty years later.
However, the Medici (as in Cosimo I's descendants) left at least three OTL opportunities for cadet branches that could've outlasted the main line:
1) Pietro de Medici, youngest son of Cosimo I, best known for murdering his first wife and cousin, Eleonora de Toledo. Pietro was a bit of a black sheep, always in debt (which his brothers didn't like paying, understandably). He married as his second wife, Brites de Lara in 1578, and had a son named Pietro (1592-1654) with her (not to mention his bastard son, Cosimino (1577-1603)), as well as three daughters - Giovanna, Caterina and Maria Vittoria, the last of whom took holy orders at the Convent of Santissima Annunziata.
2) Giovanni de Medici, legitimized son of Cosimo I by Eleonora degli Albizzi. Another black sheep, originally destined for the church and ended up in armour designing the Belvedere Fortress in Florence instead. A military man, he acquired some wealth, was a patron of the arts and sciences (and apparently, friendly with some Jews), and married the Genoese lady, Livia de Vernazza. By Livia he had two children, but since the Medici weren't keen on the whole child-support thing, they disinherited the kids (by pointing out that Livia's first husband was not really dead when she married Giovanni (or some such)), a boy, Giovanni Francesco (1619-1689) and a girl, Maria Maddalena (1621-1621) and seized Giovanni's wealth when he died.
3) Staying with disinheriting kids by previously married ladies, Francesco I married his mistress, Bianca Cappello shortly after his wife, Johanna of Austria, died. She had given him a son, and Grand Duke Ferdinando, on Francesco and Bianca's deaths, disinherited the boy, Antonio (1576-1621) by claiming that he was a changeling. That done, he pushed Antonio into the Order of Malta to prevent him having kids. Fat lot of good that did, Antonio kept a mistress, a Lucchese lady named Artemisia Tozzi, and sired five kids by her: Maria, Maddalena (1610-), Paolo (1616-1656); Giulio (1617-1670); and Antonio Francesco (1618-1659). Of these, Antonio Francesco married a girl named Maria Francesca Angietti, but there's no record of children being born; whilst Maria and Maddalena both ended up alongside their cousin as nuns at the Santissima Annunziata Convent.
I can understand the disinheritance of these kids, and, given the day and age in which they lived, I suppose poison would've been an easier method of ridding the world of them. But what if these side branches of the Medici were to form a sort of princes du sang in Florence, much like the Vendomes, the Maines and the Toulouses did at Versailles. That way, if the main branch looks like it's dying out, marry one of them (or their son) to the nearest main-line princess and do what Cosimo III wanted to do, and establish semi-salic succession. After all, it was written when the Austrians took over, that: "the Tuscans would give two thirds of what they possessed to have the Medici back, and the remaining third to be rid of the Lorrainers".
Are cadet lines possible? Could we perhaps see the Medici survive longer than to 1743? Is it possible Tuscany can recover to the extent it did under the Lorraines?