Different GPU applications exhibit varying scalability patterns with network-on-chip (NoC), coalescing, memory and control divergence, and L1 cache behavior. A GPU consists of several Streaming Multi-processors (SMs) that collectively determine how shared resources are partitioned and accessed. Recent years have seen divergent paths in SM scaling towards scale-up (fewer, larger SMs) vs. scale-out (more, smaller SMs). However, neither scaling up nor scaling out can meet the scalability requirement of all applications running on a given GPU system, which inevitably results in performance degradation and resource under-utilization for some applications. In this work, we investigate major design parameters that influence GPU scaling. We then propose AMOEBA, a solution to GPU scaling through reconfigurable SM cores. AMOEBA monitors and predicts application scalability at run-time and adjusts the SM configuration to meet program requirements. AMOEBA also enables dynamic creation of heterogeneous SMs through independent fusing or splitting. AMOEBA is a microarchitecture-based solution and requires no additional programming effort or custom compiler support. Our experimental evaluations with application programs from various benchmark suites indicate that AMOEBA is able to achieve a maximum performance gain of 4.3x, and generates an average performance improvement of 47% when considering all benchmarks tested.