To me, sorry, it doesn't make sense at all.
In the former speech you are saying, "I will show you my personal definition of a word",
while on the contrary the latter speech is saying ( or it looks like ) "I am going to
show you another cases ( = the way of saying )".
While you are concluding your own "definition" of the word, at that same time you are
saying the somewhat contradictions. ( Meaning, you decided your own "definition", you are mentioning there are variety of ways to saying it ).
My choice will be この言葉について私なりの定義を与えますが、異なる私なりの可能な定義も見てみましょう。