I have been out of touch with this area for some time. I'm sure there are more "modern" texts out there that would be fine for your purposes.
Introduction to Complex Analysis, Part 2; Functions of Several Variables by B V Shabat - acevasygotin.tk
Perhaps another responder could steer you toward them. I know there is a book by Stephen Krantz, for instance, but have no first-hand knowledge of it. Sign up to join this community. The best answers are voted up and rise to the top.
Introduction to Complex Analysis in Several Variables
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