Suppose we are diagnosing a set of symptoms of a disease. If there is only one symptom, we will give our conclusion very little weight because that one symptom could be due to random chance. However, if we see multiple symptoms, then it is probably not due to random chance but due to some cause.
This simple rule is sufficient to eliminate stochastic effects in the final decision: make decisions based on multiple observations rather than a single observation.
In a cell, a "decision" can be something like upregulating a gene. If this decision is made by a single transcription factor that detects some sort of environment, then the decision (transcription) will be noisy. In contract, if multiple transcription factors that all respond to the same environment are used, then the transcription process will be a function of the sum of multiple stochastic processes. The sum will always have a lower variance. Unfortunately, multiple regulators means the there are multiple association/dissociation events, which would add more noise. The solution would have to be a bit more clever than this, but the general idea holds.