This sound like a hierarchical hypothesis structure, in which you might want to:
- Find genes expressed in any treatment
- Find the treatment that caused the expression of a given gene.
You will typically go about by answering (1) and then (2).
For answering (1), you will want to aggregate over treatments at each gene. "How to aggregate?" depends on the error measure you wish to control. FDR control seems more appropriate in a preliminary study than FWE control. For FDR control, you can use a Simes aggregate p-value (see reference) or be conservative and use the maximal p-value over treatments. Once you have a single p-value for each gene, look for expression using the Benjamini-Hochberg procedure.
Once you have your subset of expressed genes, you can address (2) and look for the treatment that activated them. Assuming you are comfortable with FDR control, you can use a B-H procedure again, but remember to penalize for the fact you have selected those genes! This can be done by using a stricter error level within each gene; Just divide your desired error level by the number of selected genes.
Here is a reference for details.