The performance portability of parallel programs across a wide range of emerging coherent shared address space systems is not well understood. Programs that run well on efficient, hardware cache-coherent systems often do not perform well on less optimal or more commodity-based communication architectures. This paper studies this issue of performance portability, with the commodity communication architecture of interest being page-grained shared virtual memory. We begin with applications that perform well on moderat scale hardware cache-coherent systems, and find that they do not do so well on SVM systems. Then, we examine whether and how the applications can be improved for SVM systems --- through data structuring or algorithmic enhancements---and the nature and difficulty of the optimization. Finally, we examine the impact of the successful optimizations on hardware-coherent platforms themselves, to see whether they are helpful, harmful or neutral on those platforms. We develop a systematic methodology to explore optimizations in different structured classes. The results, and the difficulty of the optimizations, lead insight not only into performance portability but also into the viability of SVM as a platform for these types of applications.