You can assign a custom script to activate when an object in an asset is -clicked.
To assign a custom script to an asset
You can now activate the script by either -clicking an object in the asset in the scene view, or
-clicking the asset or an encapsulated object in the Outliner and selecting Asset from the pop-up menu.One way to use this attribute is to assign a script that adds a custom menu for a specific asset to the existing pop-up menu that appears when you -click an asset in the scene or in the Outliner (in the Asset section of the pop-up menu). An example of such a script named containerRmbMenu.mel is included with the Maya default scripts. You can find it in your Maya install directory under scripts/others.