Cross-species spillover events are responsible for many of the pandemics in human history including COVID-19; however, the evolutionary mechanisms that enable these events are poorly understood. We have previously modeled this process using a chimeric vaccinia virus expressing the rhesus cytomegalovirus-derived PKR antagonist RhTRS1 in place of its native PKR antagonists; E3L and K3L (VACVΔEΔK+RhTRS1). Using this virus, we demonstrated that gene amplification of rhtrs1 occurred early during experimental evolution and was sufficient to fully rescue virus replication in partially resistant African green monkey (AGM) fibroblasts. Notably, this rapid gene amplification also allowed limited virus replication in otherwise completely non-permissive human fibroblasts, suggesting that gene amplification may act as a "molecular foothold" to facilitate viral adaptation to multiple species. In this study, we demonstrate that there are multiple barriers to VACVΔEΔK+RhTRS1 replication in human cells, mediated by both PKR and RNase L. We experimentally evolved three AGM-adapted virus populations in human fibroblasts. Each population adapted to human cells bimodally, via an initial 10-fold increase in replication after only two passages followed by a second 10-fold increase in replication by passage nine. Using our Illumina-based pipeline, we found that some SNPs which had evolved during the prior AGM adaptation were rapidly lost, while 13 single-base substitutions and short indels increased over time, including two SNPs unique to HFF adapted populations. Many of these changes were associated with components of the viral RNA polymerase, although no variant was shared between all three populations. Taken together, our results demonstrate that rhtrs1 amplification was sufficient to increase viral tropism after passage in an "intermediate species" and subsequently enabled the virus to adopt different, species-specific adaptive mechanisms to overcome distinct barriers to viral replication in AGM and human cells.