Can I work for CVS and Walgreens at the same time?

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I'm currently working as a pharmacy tech in CVS but it's only a part time job and I'm not getting enough hours to pay for my rent. Now there's a Walgreens in the area that needs a tech ASAP since one of their techs is going home to China for vacation. Do you think it would be okay to work at both stores at the same time? I mean, isn't there any policy which prevents current CVS employees to work for Walgreens (just because they're two competing companies) and vice versa?