edge vs march on

edge is a noun but march on is not a noun.

Word	Noun	Adjective	Verb	Adverb
edge	Yes	No	Yes	No
march on	No	No	Yes	No

As verbs, march on is a hypernym of edge; that is, march on is a word with a broader meaning than edge:

Other hypernyms of edge include advance, go on, move on, pass on, progress.

edge (noun)	march on (noun)
a sharp side formed by the intersection of two surfaces of an object
the outside limit of an object or area or surface; a place farthest away from the center of something
a slight competitive advantage
the attribute of urgency in tone of voice
the boundary of a surface
a line determining the limits of an area

edge (verb)	march on (verb)
lie adjacent to another or share a boundary	move forward, also in the metaphorical sense
provide with an edge
advance slowly, as if by inches
provide with a border or edge