In "evolve-and-resequence" (E&R) experiments, whole-genome sequence data from laboratory-evolved populations can potentially uncover mechanisms of adaptive change. E&R experiments with initially isogenic, asexually reproducing microbes have repeatedly shown that beneficial de novo mutations drive adaptation, and these mutations are not shared among independently evolving replicate populations. Recent E&R experiments with higher eukaryotes that maintain genetic variation via sexual reproduction implicate largely different mechanisms; adaptation may act primarily on pre-existing genetic variation and occur in parallel among independent populations. But this is currently a debated topic, and generalizing these conclusions is problematic because E&R experiments with sexual species are difficult to implement and important elements of experimental design suffer for practical reasons. We circumvent potentially confounding limitations with a yeast model capable of shuffling genotypes via sexual recombination. Our starting population consisted of a highly intercrossed diploid Saccharomyces cerevisiae initiated from four wild haplotypes. We imposed a laboratory domestication treatment on 12 independent replicate populations for 18 weeks, where each week included 2 days as diploids in liquid culture and a forced recombination/mating event. We then sequenced pooled population samples at weeks 0, 6, 12, and 18. We show that adaptation is highly parallel among replicate populations, and can be localized to a modest number of genomic regions. We also demonstrate that despite hundreds of generations of evolution and large effective population sizes, de novo beneficial mutations do not play a large role in this adaptation. Further, we have high power to detect the signal of change in these populations but show how this power is dramatically reduced when fewer timepoints are sampled, or fewer replicate populations are analyzed. As ours is the most highly replicated and sampled E&R study in a sexual species to date, this evokes important considerations for past and future experiments.