Is it possible to change my settings such that the Taskbar Buttons that I have pinned to the taskbar do not show when the Taskbar Icon is on another taskbar?

For example: If I open IE from the button pinned to the taskbar, the icon associated with the open IE window replaces the button. However, if I move IE to my secondary monitor, the button and icon separate, leaving the button on the windows taskbar, but moving the icon to the taskbar on the secondary monitor (see photo).

Thanks!

Has there been any change to this feature?