Genetic switch systems with mutual repression of two transcription factors, encoded on plasmids, are studied using stochastic methods. The plasmid copy number is found to strongly affect the behavior of these systems. More specifically, the average time between spontaneous switching events quickly increases with the number of plasmids. It was shown before that for a single copy encoded on the chromosome, the exclusive switch is more stable than the general switch. Here we show that when the switch is encoded on a sufficiently large number of plasmids, the situation is reversed and the general switch is more stable than the exclusive switch. These predictions can be tested experimentally using methods of synthetic biology.