I too have thought about this and this is what I have done. What you might try is this.
You can install ZenCart into a new directory. EX> store1, store2
Create a second database via PHPMyadmin and go through the normal Zen installation process, manual install is far superior to auto install via control panel. Trust me. Take the time and install it yourself.
After you have the new cart set up into a second directory just "Import" the first database into the new cart. Any small changes you make can be done in each site and should not be too much trouble after you have the bulk of the products in there.
You cannot have 2 different sites using the same data as it would conflict.
I manage 3 sites all with similar product data and it is not too difficult.
Hope this helps.