In short, as many as you can get to. While venues are subject to capacity, the music schedule is designed to permit club hopping to experience as many artists as possible. Most shows begin at the top of the hour (e.g., 8:00 PM) and last 40 minutes. You then have 20 minutes to hop to the next venue (many are within walking distance) in time for the next act to start at the top of the hour (e.g., 9:00 PM).
Approximately 2,000 artists play sets between Monday, March 13 and Sunday, March 19. With a little advance planning, you can experience a whole lot of music in just 7 days.