Finding network routes based on facility attributes

I am trying to find a way to find routes between locations, based on attributes of the destination. For example, I have a shapefile of multiple destinations, each with attributes A, B, C, D. The fields are boolean and the destinations either have A or don’t, have B or don’t, etc.

Is there a way to find closest routes based on which attributes are present i.e. if I’m looking for a route to destination which has A, B, and C it will ignore nearer facilities containing just A and B?

I am using ArcMap.