Also means
to add on (figuratively)
Usage Note
Greffer in medicine means to perform a graft or transplant (greffer un rein = to transplant a kidney); in botany it means to graft a plant cutting. Figuratively, se greffer sur means to be added onto or tacked onto something else: un problème qui se greffe sur la crise (a problem added on top of the crisis). The related noun is greffe (graft, transplant) or greffon (the graft tissue/cutting).
Examples
"Les chirurgiens ont greffé un nouveau rein."
Natural Translation
The surgeons transplanted a new kidney.

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