Multiple Visibility Parameters to single object

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I currently have a generic annotation symbol of an automatic damper that we use for details and diagrams. I have it set to have visibility parameter to show as existing or new. What I'm trying to accomplish now is to have the ability of the the damper portion attached to the top, bottom, left, or right as needed with also being able to be existing or new. As you well know you can't set a single line to have multiple visibility settings, at least I can't figure it out. I have attached the revit file to this post. You will notice that it's basically the same symbol each in a different line weight. They are set directly over top of each other and set to existing or new. I am wanting to be able to have the damper portion to have a new and bottom parameter for the heavier line weight and existing and bottom for the lighter one. Is this possible or is their a work around to accomplish this?