Being a Rajdhani, the concept is National Capital to State Capital.. Hence cannot be extended to CAPE.
However, SR can plan a new weekly Rajdhani Express between Thiruvananthapuram Central to New Delhi via Nagercoil Town - Tirunelveli - Madurai - Thiruchirapalli - Chennai Egmore - Vijaywada - Ballarshah - Nagpur - Bhopal - Jhansi and Mathura