Objects do not talk to each other.
Just select all objects together at the same time and change the value of the parameter.
All those you have selected will change but should not affect other parameter values you do not change.
It can be done if you save the information in an external text file that the object can read, but you must force an update, it is not always automatic.
Another possible way is to use the Project Info and have the objects read that project info field.
You could do the same with a Library Global parameter (Model View Options) but that can get messy as each MVO scheme could have a different value for the parameter, hence the notes might change depending on the MVO saved with the view.
Or possibly create a Property that you can associate with a classification.
If the element is classified correctly, you will be able to access the value of that property.
Actually another trick similar to selecting all objects, is to use a schedule that lists all of the objects and that parameter field.
I can't remember off hand if you can select multiple objects in a schedule and edit them all at once (you can if you use the show and select on plan /3D option).
But you can select one of the objects in the schedule, change the value of the note field, then copy and paste to other objects in the schedule.
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