He has many a little cough (3)
I believe the answer is:
hem
'a little cough' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'he has many' is the wordplay.
'has' means one lot of letters go next to another.
'many' becomes 'm' (Roman numeral for a thousand).
'he'+'m'='HEM'
Can you help me to learn more?
(Other definitions for hem that I've seen before include "Part of skirt" , "Express hesitation" , "Double-backed cloth border" , "Border; fringe" , "It draws attention to" .)