You could try jittering the points slightly. See this blog post for some help with the calculations (Jitter those points! )
If you're mapping using the Tableau geocoding zip codes and want to jitter the data, you'll need to make an extra step and export the lat/lon centroids for the zip codes (just select all the points, view the data, export, and join the table of results with the generated lat/lon values back into your data in Tableau...though I'd recommend deleting everything except for zip code and lat/lon values in the CSV before you do that just to keep thinks a little cleaner).
Another option to explore would be to add a viz in tooltip (Create Views for Tooltips (Viz in Tooltip) ) so that when you mouse over any zip code, you'll see a breakdown of the stores in the zip code in the tooltip. This would make it so that you didn't have to jitter the points. You would still just have one point in each zip code, but the mouse over would give you stats from all points in the zip code - no asterisk to deal with...