Avoid double count of points on intersection with polygon

[yockee]

I want to count some houses that are within administrative boundaries. The problem is, that some houses sit on the borderline of 2 or more polygon boundaries. I want to avoid double counts.

This is the ilustration:

What I want to achieve, for example:

Poly 1 contains 4 buildings.
Poly 2 : 3.
Poly 3 : 3.

So, in total, there are still 10 buildings.

How can I achieve this?

[DanPatterson]

With something like 'select by location' it may be the case where you have to compare 2 runs of the tool with

'within' versus 'within Clementini'

Select By Location graphic examples—ArcGIS Pro | Documentation

in the Clementini case, points exactly on a boundary aren't counted, so you could isolate those points and modify the number counts for the alternate method