Hoping these ideas might be helpful:
1) Most tools work on a selection set, so you could do a query to select features with the same ID and then summarize distances.
2) If there are lots of clustered IDs and you don't know ahead of time what the values will be, you can create a model to loop through all of the unique values in a field (the ID field) and process them. You would use the Field Value iterator in Model Builder.
3) Near table might provide the summary information you need.
4) If you run the Near tool to add a field with the distance to each feature's nearest neighbor, you could then run Summary Statistics, group by ID (case field) and compute the average, minimum, range, etc. statistics for each cluster (in other words, summarize on the Distance field created when you ran Near).
Perhaps one of these solutions will work. Hope so.
Best wishes!
Lauren Scott
Esri