Mendelian randomization is a versatile tool to identify the possible causal relationship between an omics biomarker and disease outcome using genetic variants as instrumental variables. A key theme is the prioritization of genes whose omics readouts can be used as predictors of the disease outcome through analyzing GWAS and QTL summary data. However, there is a dearth of study of the best practice in probing the effects of multiple -omics biomarkers annotated to the same gene of interest. To bridge this gap, we propose powerful combination tests that integrate multiple correlated $P$-values without assuming the dependence structure between the exposures. Our extensive simulation experiments demonstrate the superiority of our proposed approach compared with existing methods that are adapted to the setting of our interest. The top hits of the analyses of multi-omics Alzheimer’s disease datasets include genes ABCA7 and ATP1B1.