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fatten (someone or an animal) up (with something)
to use something to make someone or an animal fat. We will fatten the calf up with corn. I don't know why they keep fattening up their children with so much food.
fatten up(on something)
1. Lit. to get fat by eating something, The cattle fattened up on the succulent grass. The bears have to fatten up on food before they hibernate for the winter.
2. Fig. to become prosperous because of something. The corporations fattened up on easy profits and low taxes. The directors of the company fattened up even during the recession when the workers were laid off.