Self-obsessive? Mad? Come again? (9)
I believe the answer is:
egomaniac
'self-obsessive?' is the definition.
I can't tell whether this defines the answer.
'mad? come again?' is the wordplay.
'mad?' indicates an anagram (I've seen 'mad' mean this).
'come'+'again'='comeagain'
'comeagain' is an anagram of 'EGOMANIAC'.
Can you help me to learn more?
(Other definitions for egomaniac that I've seen before include "Oneself, one would love" , "number one fan" , "Excessively self-concerned person" , "Come again (anag.)" , "Abnormally egotistical person" .)