This one has interesting possibilities; Margaret's devout and fellow education enthusiast friend Bishop John Fisher (exec by Henry VIII for loyalty to the Papacy in 1535 and made a saint), who helper her to set up a college in Cambridge), spoke of her having difficulty in giving birth to Henry VII aged 13 and not conceiving again so possibly if she had been born earlier (1441 not 1443?) she could have had less problems and had a son by Henry Stafford in the 1460s. Even a daughter would have been useful, as marriageable to a family ally of the Staffords or of Margaret's third husband Thomas Stanley - and thus providing a son , born c. 1490?, to be a later ally and boon companion of his cousin Henry VIII. A son of this man, born c. 1515-20?, would then be available and semi-royal as a potential husband for Princess Mary if her engagements abroad failed in both the 1520s (before she was declared a bastard) and after Henry reinstated her in the line of succession and offered her around as a husband after 1536 - if Henry was not obsessed with the idea that an English lord would be 'beneath' her socially and also a security threat. (He initially objected to his younger sister Mary remarrying to his close but at that point non-aristocratic friend Charles Brandon in 1515 after her husband Louis XII of France died.) .
It would seem likely that if Margaret Beaufort and Stafford had a son, 'John?', in the 1460s he would be available to be engaged to an ally of the Staffords or the Stanleys pre-1483, when Thomas Stanley was seen as a loyal Yorkist and ally of Edward IV - who Margaret was ostentatiously loyal to in the 1470s, while trying to get Edward to recall her eldest son Henry Tudor from Brittany. (Edward is supposed to have offered HT the hand of his eldest daughter Elizabeth to lure him back, but this might have been a trap to get Lancastrian pretender HT in his hands and into the Tower or safely married off to a low-status bride and 'disqualified' as a threat instead; he was devious enough.) Thomas Stanley was a long-term Yorkist, though as became well known a selfish and unreliable character, and had deserted his brother-in-law and first patron Warwick in 1471 to back Edward as E invaded England; Edward would probably have used a younger son of Margaret Beaufort (son or stepson of Stanley) as yet another pawn in his intricate marital alliance plans and married him off to some useful noble ally's daughter, choosing a reliable Yorkist to 'control' him. Possibly a junior and Yorkist relative of a rising dynasty dependant on Edward for patronage - a Herbert from SE Wales (related to E's late strongman there who Warwick had killed in 1469, William Herbert Earl of Pembroke), as a local noble semi-neighbour of the Lancs Stanleys, a junior Howard , or a Yorks or Lancs ally of the Stanleys. if the young 'John Stafford' was not married but just engaged as of 1483-5, Richard III then could have used him as bait to lure in another potential noble ally and dangled preferment in front of him to get him to keep an eye on his ex-plotter mother and the distrusted Thomas Stanley. If 'John' was not married as of post-1485, Henry VII and Margaret would have used him as a link to some useful Lancastrian or ex-Yorkist family as in OTL Margaret used Henry's wife's sisters - eg the Welles or the Howards?
A semi-royal son of 'John's could be a marital partner for Mary Tudor or, after 1536, a fiancee for Elizabeth - if Henry VIII did not extend his suspicion of allegedly ambitious and arrogant cousins with royal blood to him , as he did in OTL to the then Duke Edward Stafford of Buckingham (son of the 1483 rebel Henry Stafford, Duke of B, executed by Richard III). It was alleged that the greedy Wolsey, annoyed by Edward sneering at him as an Ipswich butcher's son, caused his ruin and execution in 1521 by playing on Henry's paranoia - but if our 'John Stafford', then in his 50s or early 60s, and his son were friendly to Wolsey - after a family row with the land-hoarding Edward Stafford? - they could have been put forward by Wolsey as potential royal marital partners. All would depend on whether they backed Catherine of Aragon against the Boleyns after 1527 and so incurred Henry's enmity, as his Courtenay and Pole cousins did in OTL; if they backed the Boleyns, they could still have been at court and in favour after c. 1536 and so been able to provide a potential husband for one of Henry's daughters. As Mary was offered the higher-ranked (foreign royal) fiances in OTL after 1536, and was acceptable to European dynasties as daughter of a legitimate wife not of the 'whore' and 'bigamous marriage' partner Anne Boleyn, Henry - or Edward VI's regents after 1547 could have found nobody wanting Elizabeth and chosen a Stafford instead out of desperation. Best chances of this if Henry had been in better health and lived after 1547, into Elizabeth's mid-teens, or Protector Somerset wanted to get rid of Elizabeth by marrying her to a loyal ally after her suspicious behaviour with his treacherous brother Admiral Thomas Seymour in 1548? Or even Mary as Queen surviving longer and 'dumping' Elizabeth on a loyal Stafford cousin if she and Philip found that no fastidious European Catholic prince wanted a 'Boleyn bastard'?