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We prove one side divisibility of the Iwasawa-Greenberg main conjecture for Rankin-Selberg product of a weight two cusp form and an ordinary CM form of higher weight, using congruences between Klingen Eisenstein series and cusp forms on GU(3, 1), generalizing earlier result of Wan to allow non-ordinary cusp forms. The main result is a key input in Wan’s proof for Kobayashi’s ±-main conjecture for supersingular elliptic curves. The new ingredient here is developing a semi-ordinary Hida theory along an appropriate smaller weight space, and a study of the semi-ordinary Eisenstein family.