GPUs achieve high throughput and power efficiency by employing many small single instruction multiple thread (SIMT) cores. To minimize scheduling logic and performance variance they utilize a uniform memory system and leverage strong data parallelism exposed via the programming model. With Moore's law slowing, for GPUs to continue scaling performance (which largely depends on SIMT core count) they are likely to embrace multi-socket designs where transistors are more readily available. However when moving to such designs, maintaining the illusion of a uniform memory system is increasingly difficult. In this work we investigate multi-socket non-uniform memory access (NUMA) GPU designs and show that significant changes are needed to both the GPU interconnect and cache architectures to achieve performance scalability. We show that application phase effects can be exploited allowing GPU sockets to dynamically optimize their individual interconnect and cache policies, minimizing the impact of NUMA effects. Our NUMA-aware GPU outperforms a single GPU by 1.5×, 2.3×, and 3.2× while achieving 89%, 84%, and 76% of theoretical application scalability in 2, 4, and 8 sockets designs respectively. Implementable today, NUMA-aware multi-socket GPUs may be a promising candidate for scaling GPU performance beyond a single socket.