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Wiktionary
border on

vb. (context intransitive English) To be almost like some other thing.

WordNet
border on

v. come near or verge on, resemble, come nearer in quality, or character; "This borders on discrimination!"; "His playing approaches that of Horowitz" [syn: approach]

Usage examples of "border on".

Though artificial construction of the ovum itself, with the proper DNA chains, seems now to be so difficult as to border on the verge of impossibility.

My guess is that the GIR is going to come boiling out of their staging areas tomorrow and be right up on the border on the 1st.