Simultaneous tests of a huge number of hypotheses is a core issue in high flow experimental methods such as microarray for transcriptomic data. In the central debate about the type I error rate, Benjamini and Hochberg (1995) have proposed a procedure that is shown to control the now popular False Discovery Rate (FDR) under assumption of independence between the test statistics. These results have been extended to a larger class of dependency by Benjamini and Yekutieli (2001) and improvements have emerged in recent years, among which step-up procedures have shown desirable properties. The present paper focuses on the type II error rate. The proposed method improves the power by means of double-sampling test statistics integrating external information available both on the sample for which the outcomes are measured and also on additional items. The small sample distribution of the test statistics is provided and simulation studies are used to show the beneficial impact of introducing relevant covariates in the testing strategy. Finally, the present method is implemented in a situation where microarray data are used to select the genes that affect the degree of muscle destructuration in pigs. A phenotypic covariate is introduced in the analysis to improve the search for differentially expressed genes.