Multiple testing, FDR and power Suppose that I've a data with a total of 30,000 observations. Each observation has a total of 6 values, 3 per condition. I'm interested in, let's say, testing if the means of these two conditions for each of these observations are different or not. For this, we typically apply a statistical test of choice to each of these 30K observations. In order to control the false positive rate due to multiple testing, we'd control for FDR at say 5% using BH method.
Example of an observation would be:
# dummy data
Condition 1: 40, 55, 48
Condition 2: 129, 77, 181

Also, let's assume I obtained a total of 1000 "significant" results. If I filter the data somehow, say, remove all those observations where the maximum value across all 6 values is < 5 and end up with a filtered set of 20K observations, then I find that the number of significant results is a bit higher, say 1250. If I continue this approach of filtering data with higher and higher thresholds (< 10, < 20 ... preferably using quantile = 0.1, 0.2, 0.3 etc..), I find that the number of significant results at 5% FDR keeps increasing up to a certain point and with too stringent filtering starts to reduce again. 
It's fairly obvious that in controlling the FP in a multiple testing setup one compromises for the statistical power. My question is, are there methods that could somehow compute a filtering criteria which maximises the power (to detect after FDR correction)? If not, is it statistically sound approach to try and filter data with more than 1 value and decide on the one that maximises significance?
 A: Applying a filter to the data is clearly a case of selective inference (a.k.a. double dipping, data snooping, etc.)
If you are removing true null hypotheses, you will have an anti-conservative FDR.
If you are removing true alternative hypotheses, you will have a conservative FDR.
The filtering criterion you are using seems "fair" a-priori in the sense it does not seem to be correlated with the truthfulness of a hypothesis. 
On the other hand, the fact that you are making more and more discoveries suggests that high response values, might also be correlated with a difference between groups. I thus suspect your filtering step will have increased the FDR of the BH procedure. Try testing it using a simulation.
Also, could it be you are using an analysis that assumes homoscedasticity where the variances actually grow with the means?. If this is the case, try some non-parametric test to compare the groups. 
Finally, back to the original question: I guess it should be possible to find the optimal number of hypotheses to test using the BH procedure. You will naturally need to define a generalized notion of power (say, average power over hypotheses). You will need to know the proportion of true null hypotheses and the power of each marginal test. 
