In terms of plot, something entirely new. I think the strength of Beyond was that it had many call-outs (especially to Enterprise) , but the plot did not revolve around them. That was the huge issue with Into Darkness. I think if they did another "let's take a new look at episode X" I'm not confident they would be able to pull it off. It's one thing for IDW to do it, but another thing for the movies.
Something new. And no re-reboot just to satisfy the people who aren't supporting the franchise anyway.
And yet, Into Darkness made a ton of moolah at the box office compared to Beyond (but I loved both films anyway.) I agree with you about having no re-reboots.