Y chromosomes often contain amplified genes which can increase dosage of male fertility genes and counteract degeneration via gene conversion. Here we identify genes with increased copy number on both X and Y chromosomes in various species of Drosophila, a pattern that has previously been associated with sex chromosome drive involving the Slx and Sly gene families in mice. We show that recurrent X/Y co-amplification appears to be an important evolutionary force that has shaped gene content evolution of sex chromosomes in Drosophila. We also demonstrate that convergent acquisition and amplification of testis expressed gene families are common on Drosophila sex chromosomes, and especially on recently formed ones, and we carefully characterize one putative novel X/Y co-amplification system. We find that co-amplification of the S-Lap1/GAPsec gene pair on both the X and the Y chromosome occurred independently several times in members of the D. obscura group, where this normally autosomal gene pair is sex-linked due to a sex chromosome - autosome fusion. We explore several evolutionary scenarios that would explain this pattern of co-amplification. Investigation of gene expression and short RNA profiles at the S-Lap1/GAPsec system suggest that, like Slx/Sly in mice, these genes may be remnants of a cryptic sex chromosome drive system, however additional transgenic experiments will be necessary to validate this model. Regardless of whether sex chromosome drive is responsible for this co-amplification, our findings suggest that recurrent gene duplications between X and Y sex chromosomes could have a widespread effect on genomic and evolutionary patterns, including the epigenetic regulation of sex chromosomes, the distribution of sex-biased genes, and the evolution of hybrid sterility.