Original User: pmcatnip
I dunno about connecting to the nearest streets but you can use Excel equations to automatically narrow down your spider diagrams/near tables to the nearest X number points. To do this each line should have a unique ID, length (or distance if a near table), and the ID of the origin rail. These should all already be there by default. Copy/paste your attribute table into Excel. Sort the data by two levels, first the origin rail ID then the length. In new columns to the right there are several options as to equations to find the nearest three (or whatever).
I'm thinking along the lines of assigning each row a value for the nearness ranking. The closest point would be 1, next point is 2, next point is 3 and so on. Here is an example. The equation in Column D checks if the origin ID is the same, then for each row associated with that origin gives it a rank according to the length. Then repeats for the next origin ID. The equation in Column E determines which rows to keep based on specifying however many you want.
[ATTACH=CONFIG]24582[/ATTACH]
Now back in GIS, you can do a table join to add the Keep field to your data using OID as the link. Select attributes with Keep = yes and export to a new layer. (EDIT: Actually the Keep field is unnecessary if you join the Near_Rank field instead and Select Attributes for Near_Rank =< 3. That may be more useful because you can change your mind at any time and export new layers with however many closest points you need.)
There is surely a way to script it in GIS using loops, or use IF statements in the field calculator, but in my opinion this is simpler.