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Genome-wide association studies (GWAS) have identified thousands of genetic variants that are associated with complex traits. However, a stringent significance threshold is required to identify robust genetic associations. Leveraging relevant auxiliary covariates has the potential to boost statistical power to exceed the significance threshold. Particularly, abundant pleiotropy and the non-random distribution of SNPs across various functional categories suggests that leveraging GWAS test statistics from related traits and/or functional genomic data may boost GWAS discovery. While type 1 error rate control has become standard in GWAS, control of the false discovery rate can be a more powerful approach. The conditional false discovery rate (cFDR) extends the standard FDR framework by conditioning on auxiliary data to call significant associations, but current implementations are restricted to auxiliary data satisfying specific parametric distributions, typically GWAS p-values for related traits. We relax these distributional assumptions, enabling an extension of the cFDR framework that supports auxiliary covariates from arbitrary continuous distributions ("Flexible cFDR"). Our method can be applied iteratively, thereby supporting multi-dimensional covariate data. Through simulations we show that Flexible cFDR increases sensitivity whilst controlling FDR after one or several iterations. We further demonstrate its practical potential through application to an asthma GWAS, leveraging various functional genomic data to find additional genetic associations for asthma, which we validate in the larger, independent, UK Biobank data resource. Author summary: Genome-wide association studies (GWAS) detect regions of the human genome that are associated with various traits, including complex diseases, but the power to detect these genomic regions is currently limited by sample size. The conditional false discovery rate (cFDR) provides a tool to leverage one GWAS study to improve power in another. The motivation is that if two traits have some genetic correlation, then our interpretation of a low but not significant p-value for the trait of interest will differ depending on whether that SNP shows strong or absent evidence of association with the related trait. Here, we describe an extension to the cFDR framework, called "Flexible cFDR", that controls the FDR and supports auxiliary data from arbitrary distributions, surpassing current implementations of cFDR which are restricted to leveraging GWAS p-values from related traits. In practice, our method can be used to iteratively leverage various types of functional genomic data with GWAS data to increase power for GWAS discovery. We describe the use of Flexible cFDR to supplement data from a GWAS of asthma with auxiliary data from functional genomic experiments. We identify associations novel to the original GWAS and validate these discoveries with reference to a larger, more highly-powered GWAS of asthma. [ABSTRACT FROM AUTHOR]