This is just for pure speculation, for people to discuss what might have happened, and what we would have liked to happen, had the show gone on for more seasons. What follows are some things I would have done if the show went on.
To begin, there are all those prospective pairings that could build into love, and it would be interesting to see them blossom as well as the new business ventures that many characters are taking. Also, Tim Grey was notably absent as Lord Merton turned his back on Larry and Amelia. It'd be nice if he might reach out to his dad and actually find himself growing closer to Isobel - she a mother who lost her son, he a son who lost his mom. I'm glad Merton turned his back on Larry and Amelia, though I do wish he would have disinherited them properly so they couldn't inherit his title. Perhaps Larry and Amelia could fail in running their family estate. But I admit, Lord Merton proved love is important.
In terms of historical events, the Great Depression and World War II would be big focuses I imagine. With the Depression so many characters would be faced with keeping their businesses afloat: Downton, Brancaster, the Sketch, Yew Tree Farm, Talbot & Branson, Mrs Patmore's Bed & Breakfast. Perhaps with World War II I imagine the family would take roles in supporting the war. Downton might become a convalescent home again, or even Brancaster. The younger generation would be the ones fighting. I'll discuss them later. Before that, with the rise of Hitler the Sinderbys I'm sure would take an active role in helping Jewish refugees from the continent.
Other historical events that could be mentioned or discussed could be the Spanish Civil War, Lindbergh's 1927 Atlantic flight, as well as the death of George V and then Edward VIII's abdication. Downton's table could include diplomats from Spain, Japan, and even Nazi Germany. The latter would be one that no one wants but cannot escape if it happened. The Sinderbys, if they were there, would be horrified. Imagine if the Nazi diplomat turned out to be directly responsible for Gregson's death! Maybe the Spanish diplomat could mention a writer named Ernest Hemingway in conversation somehow (since Hemingway reported on the war which inspired For Whom the Bell Tolls).
Now to the new generation, whose lives would begin to take center stage more as they grew older. Bates and Anna's son would be named Edward, Oliver, or Christopher, with his middle name being Robert. The unborn child of Henry and Mary would be a girl whose middle name is Anna. Her first name would be either Prudence (after Lady Shackleton) or Charlotte (after Charlie Rogers). Edith and Bertie would have a son and heir. Edith would think of Gregson no doubt and having Marigold while pregnant, and Bertie seeing this once the boy is born suggests his name be Michael. Edith would then select Peter for a middle name, in honor of Bertie's cousin. The family would nickname him Mike. Then, in addition to Rose's daughter Victoria, she'd have two twin boys, David Hugh and Joseph Daniel. We could have a case of the good twin and bad twin, or Victoria could be the bad one - namely a wild card worse than Rose was, and Rose would have to sow her wild child's oats.
The girls would go to the school where Rosamund is a trustee. The boys would make three friends at university, whose names we already know: Charlie Bryant (Ethel's son), Daniel Clark (Lord Sinderby's illegitimate son), and Fred Moorsum (Jane's son). Fred, the oldest, could already be a professor of math (as he was mentioned as being skilled at it). Charlie and Daniel would become the respective beaus of Sybbie and Marigold. Charlie, like Sybbie, could relate to having had a parent who was looked down upon because of their background - he would love his mom deeply and fiercely defend her against those who speak ill of her because of what she did to help him. His grandfather might not approve as she is a devout Catholic, but Charlie might be drawn to Catholicism. When his grandpa dies and with his grandma's blessing (he was closer to her), he would convert for Sybbie. Tom might overhear Charlie tell her "I'd wait forever".
As for Marigold and Daniel, I imagine they'd both find out they are love children. Marigold could surprise everyone by revealing she'd worked it out long ago and her love for her family unwavered. Daniel might be more upset, as would Lord Sinderby's family, but Marigold could help them all make amends, and Daniel would love her even more.
With the war, the boys would all enlist no doubt. Perhaps Charlie could be a medical student and serve in the medical corps, as Sybbie would be following in her mother's footsteps as a nurse. Marigold would help out at the Sketch, to which she is sole heir as Mike is heir to Brancaster, reporting on and supporting the war. Daniel could be interested in journalism or creative writing, like Gregson was. Fred Moorsum might go to Bletchley Park to serve in military intelligence.
Beyond World War II, I don't know how much longer it would go though, at least for me. I haven't thought that far. Feel free to discuss your own opinions. And if anyone writes fanfiction and wants to use my ideas, feel free to do so. I don't write fanfic and won't sue.
I'm sad the show ended, but I'm glad it ended well for the characters.