No, it is not possible. Points are displayed based on Point and Point Label Styles. Therefore, if you want a SELECT group of points to have unique display properties, then you need to create a unique point label style. Otherwise, if you edit the point label style already being used, you will change all points using this style.
The point label style will control the text style used, as well as the layout and dragged state components and displays (text formatting, layers, borders, arrows...).
The point style will control the marker format and the display of markers and labels (visibility, layer, color...)
Hope this helps...
Charlie Ogden, PE - Application Engineer
(800) 336-DESK (3375)
Microdesk is the leading provider of Architectural, Civil/Survey and GIS/FM
solutions based around Autodesk and ESRI technologies.