ME A LARK = I a bird. Mealark is a large container for oats.
or it could be ME (for I) + A + L (for large) + ARK (for chest) although not sure where bird comes in. Anyway, as usual Kayakamina came up trumps, who I thank profusely.
I'm sure Kayakamina knew, and was talking about this anyway, but I'll throw in my reasoning for the word play. "Cases" in the clue refers to grammatical cases of the pronoun "I". In the nominative "I", but in all other "cases" the word ME is used e.g. ACCUSATIVE He hit ME. DATIVE = (to) me, etc. So "In other cases I = ME. "will go with a bird" A LARK. Definition is "a large chest" ME + ALARK.