Dog, or part of one (4)
I believe the answer is:
sole
I believe this is a triple definition!
'dog' is the first definition.
(thesaurus)
'or' is a link.
'part' is the second definition.
(sole is a kind of part)
'of' acts as a link.
'one' is the third definition.
(synonyms)
(Other definitions for sole that I've seen before include "Underside of the foot" , "Just one - fish" , "fish > that's never less than foot in length" , "fish in the sea!" , "Exclusive class of fish" .)