Yes, trivially. If private key d has public key X coordinate m, then so does private key n-d, where n is the order of the curve (as n-d equals -d modulo n).
This follows from a basic rule in elliptic curve point arithmetic: -(x, y) is defined as (x, -y). From this is follows that if dG = (x, y) then (-d)G = (n-d)G = (x, -y) = (x, p-y).
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