The next stage from the rusine to the cervine or elaphine type is the rucervine.    From Wordnik.com.  [Natural History of the Mammalia of India and Ceylon] Reference

The next phase of development of which we have examples in India is the true cervine or elaphine type of horn in which the brow-tine is doubled by the addition of the bez; the royal is greatly enlarged at the expense of the tres-tine, and breaks out into the branches known as the sur-royals.    From Wordnik.com.  [Natural History of the Mammalia of India and Ceylon] Reference