Yes, you can install Zen Cart on the same server as another shopping cart. To be safe, before installing Zen Cart you should back up your other program and its database. You should also install Zen Cart in its own directory while setting up and testing. The Zen Cart database should be installed in a fresh database.
DO NOT INSTALL ZEN CART IN THE SAME DATABASE AS ANOTHER SHOPPING CART PROGRAM. YOUR DATABASE TABLES COULD BE OVERWRITTEN OR CORRUPTED.