The Scots Princesses
James I of Scotland really made some good matches for his daughters (especially when one considers how the rest of Europe viewed Scotland at the time), namely:
Margaret - married the Dauphin (future Louis XI) of France.
Isabella - married the duke of Brittany and during her widowhood was considered for Carlos of Aragon, Prince of Viana.
Mary - married Wolffert VI van Borsellen.
Annabella - married the Savoyard count of Geneva.
Eleanor - married Archduke Sigmund of Austria.
Margaret had no children by her husband, Isabella only had two daughters, Mary's two children both died in infancy/young, Annabella was twice married and twice divorced with children by her Scots second husband, and Eleanor died in childbirth with her only child, a son.
But say their marriages into the courts of Europe had been more successful, if (or when) the War of the Roses broke out, there would then have been more Lancastrian (albeit Beaufort descended) heirs floating around. What might the results of that have been?