Treatment resistance due to tumor heterogeneity is an ongoing problem for maintaining a sustained response to treatment. Regardless of their lineage, heritable phenotypic adaptions may be beneficial for the tumor to respond to stepwise changes in the environment during tumor growth. There may be further benefit for cells to develop the trait of being adaptable - to respond to large shifts in the microenvironment and survive metastasis to a new organ or fluctuations due to treatments. Genomic instability may aid large changes in phenotype and promote growth, but there may be limits. With too much mutation and deviation from the parental phenotype, cells lose important regulatory and maintenance functions necessary to survive. So is there an optimal rate of evolvability? We use an off-lattice agent-based model to investigate how the rate of change through phenotypic trait space affects tumor growth and response to treatment. We assign cells with different combinations of proliferation rates and migration speeds and test how the variance from the parental cell on division affects the selection of trait combinations over time. During growth, heterogeneity is gained quickly and space matters less if evolvability is forced to continually increase, but there is more selection for proliferative phenotypes and slower evolvability if its rate is allowed to drift by increasing or decreasing. We compare responses to continuous, intermittent, and adaptive treatment schedules of an anti-proliferative drug. Tradeoffs generally imposed a greater selection force leading to faster recurrence. Increasing the deleterious effect of evolvability through an increased death rate could select for drug sensitive cells with less variability.