So as I understand your requirements the answer here is that this is possible.
Consider the below point data provided as a Web Map Service and accompanying GetFeatureInfo request window for some point location showing all the attributes in the underlying shapefile.
Now instead of a WMS you could instead (or, as in this case, as well) provide a WFS. In this case if we look at the DescribeFeatureType response we can see all the attributes are available.
DescribeFeatureType request for a point data set
And a GetFeature response looks like:
These example services are provided by MapServer but there's nothing special here to prevent it being set up in ArcGIS, GeoServer, or any other WFS server software. You'll just need to pull all the required data (Points and additional data into a single data source).