Hi Sweta,
yes we can add we can our own items under "Assigned To" in IC InBox. For this we need to implement the CRM_IC_INBOX_BADI badi method MANIPULATE_RESP_DROPDOWN_LIST for your new requirement.
If user is assigned to a org unit, standard will display only 3 options 1. Me, 2. My Group 3. Org unit which agent is assigned. If the user is assigned to high positions like Area manager or Head of the Area, then we need to enhance the above said method and upend c_responsibles and c_org_units table with the required values to display the options in the drop down.
Thanks,
Kiran Vemula.