I don't think there's that much more of a story besides the one told in the intro and the guys talking in the Carrotian Council.
It's basically just one poor guy who lost his nose (like Voldemort) killing innocent, mind-tricked fruits on his quest to get his carrot nose back - which is probably long rotten when he finally gets it since it takes the average player at least a few months to get it.
Then there are the few guys who were first to defeat Tuberculos to regain their noses (Why does he always steal carrot noses from poor snowmen? So evil

) who decided to hide in a parallel dimension long before the great update (which probably is the opening of the pds for everyone) to wait for you and me and help us to defeat Tuber ourselves.
But they are not half as helpful as they think they are. All they tell is that the Bobble Cane, which is at the end of the pd, has got great powers and that you should retrieve it. What those powers are remains a mystery.
I'm also not sure what the cane is doing in that pd. It either got stolen by the blobs or it has spawned the blobs. Both options I don't find too great. Or the members of the Carrotian Council actually use the blobs to protect the bobble cane.
You also may ask if - since the members of the Carrotian Council, as they say, fought Tuber in another dimension - there are different Tubers in different dimensions or if Tuber can travel around between different dimensions.
And how comes that he still has got a carrot in his chamber, even after you've collected it?
Questions over questions ...
