Hi Dan,
Thanks for the suggestion, but Nearest Neighbor only calculates the average distance of the first nearest neighbor for a set of points.
I did, however, end up finding an awesome tool that does exactly what I was looking for. It's called Generate Near Table: https://pro.arcgis.com/en/pro-app/3.1/tool-reference/analysis/generate-near-table.htm
It does the same thing as Nearest Neighbor, but you can specify how many neighbors that you'd like to have distance calculated for from each point (e.g., give me the distance of each of the 10 nearest points, or 50 nearest points).
I've attached a map image called "100 nearest neighbors for two different points" that illustrates this.
Each of the orange points is the center of a potential open territory that an animal starting at one of the blue points could disperse to. The red lines connect this starting location to the boundaries of the 100 closest territories (represented by gray polygons).
The blue point labeled 4333 has many potential territories in a relatively small area. However, the animal that starts at point 6669 has to cover a larger area to find 100 potential territories. The generate near table calculates the distance from each of the orange points to it's 100 closest territories and ranks them 1-100 based on their proximity.
All kinds of fun analyses can be done with the new data table. My data set had ~45,000 points, so when I ran the tool it created a new point file with nearest neighbor distances for each point's 100 closest neighbors, I ended up with a table with ~45 million records. Amazingly, this tool only took about 2.5 minutes to run.
Hope this is helpful for anyone trying to do something similar. The output table has xy coordinates for both the FROM and TO points, which allows you to create the connector lines in this attached map using the xy to point tool.