statistically it depends on whether tests are independent; i.e. if the cause of the false positive is to do with the subject then using three tests won't help.

statistically it depends on whether tests are independent; i.e. if the cause of the false positive is to do with the subject then using three tests won't help. if the cause of the false positive is entirely random then doing three tests will help improve the accuracy. if the correlation between false positive occurrence and the testing parameters are somewhat correlated then it may help but maybe not as much as you'd want.