The Intermediary Grimoire is a Grimoire that allows a person to transfer abilities between living things. Mai Natsume was briefly this Grimoire before losing the ability after the No-Name Grimoire fused with her heart to become a Remix Heart.
By kissing someone, Mai was able to copy their powers or techniques and pass them onto someone else, again by kissing. The first time she did this was by transferring Noel Vermillion's "death dinner" cooking onto Taro Sasaga'e. [1] Eventually, he lost the ability. Personalities can also be seemingly transferred, as she was able to give a Torifune panda the personality of Shiori Kirihito. [2]
Generally speaking, Mai could take someone's attributes by just tasting them, not necessarily needing to kiss them. [3] She lost this ability when she became a Remix Heart. [4]