It could be that the 13th Doctor stumbles upon a remnant of Rose's timeline during one of her adventures. Maybe a powerful entity intentionally brings them face to face for a specific purpose.
Maybe during a battle against a common enemy, forcing them to team up. That's when Jack meets 11.
Well, Jack might meet the 11th Doctor when there's a threat to the space-time continuum that requires their combined efforts to fix. Or it could be a chance encounter at a pivotal moment in history.
It's possible that Jack meets the 10th Doctor when they are both drawn to a mysterious energy source. Another scenario could be when they are brought together by a common enemy with a devious plan.
It could lead to all sorts of adventures and unexpected plot twists. Maybe there's confusion at first but then they team up to save the universe!
They could meet during a time-traveling adventure gone wrong, getting stranded in the same era.
Yes, in many fanfictions, Clara has deep feelings for the 12th Doctor.
There are various plots. Sometimes they might face dangerous aliens or get trapped in perilous time loops that cause them harm.
Often, these fanfictions might involve one of them getting injured or facing a difficult situation, and the other providing support and solace. It could also be about internal struggles and how they find comfort in each other's presence.
I can recommend 'The Time Healed Wounds' - it's a great one where they comfort each other after a particularly tough adventure.
In many fanfictions, River's meeting with the Thirteenth Doctor is often a creative and unexpected encounter, full of surprises and adventure.