Thorin in the Blue Mountains

[Inziladun]

Originally Posted by Kuruharan

I'm not proposing that significant populations of Broadbeams and Firebeards existed, but that their royal lineages did and there were enough remaining members to sustain distinct communities. Tolkien nowhere said all dwarves abandonded the Blue Mountains after the First Age, just "most."

I'm inclined to think that if there were remnants of the other Dwarven lines in the Ered Luin in the Third Age, they were so small as to be really just settlements, nothing as grand as kingdoms.
Since Thorin's line was of the Longbeards, making him Durin's heir, I doubt Dwarves of other houses would have had much of a problem sharing the mountains with his own relatively small people.