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The MugMugs can be bred using a clay ball. This is their food and is used for all of the MugMug variants. Each MugMug variant requires their own unique items to tame and saddle them. these items are as follows:

Taming:

MugMug - Suspicious Stew

MelonMelon - Melon Slice

CowCow - Milk Bucket

BrickBrick - Brick

Saddling:

MugMug - Bowl

MelonMelon - Melon

CowCow - Oak Log

BrickBrick - Cracked Stone Bricks