If an employer can't/won't give you enough hours to survive it shouldn't be a problem to pick up extra work.
A smart employer would use this to their advantage, slyly drawing information from you about the competition.
But, many fail to see competition as a good thing, so no one can really answer this but you, and maybe only after the fact.
Myself, I would go to my Chef and explain the situation and see how he/she responds.
Make sure you mention all of your positive feelings about the place and explain that you are only considering this, and only for financial reasons.
Good luck.
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You should have been here when the shiitake hit the flan! | 
