How to deal with a late K1

I invested in a real estate fund where I would receive a K1. However, the managing company said that the K1s may arrive after April 15, and could be even as late as Sept. 15.

 

Is it appropriate to file for an extension, or an amended return? Is one way better or the other? Does it matter if my distributions were smaller (say less than $1000) or larger (more than $1000)?