The study of fitness landscapes, which aims at mapping genotypes to fitness, is receiving ever-increasing attention. Novel experimental approaches combined with NGS methods enable accurate and extensive studies of the fitness effects of mutations - allowing us to test theoretical predictions and improve our understanding of the shape of the true underlying fitness landscape, and its implications for the predictability and repeatability of evolution. Here, we present a uniquely large multi-allelic fitness landscape comprised of 640 engineered mutants that represent all possible combinations of 13 amino-acid changing mutations at six sites in the heat-shock protein Hsp90 in Saccharomyces cerevisiae under elevated salinity. Despite a prevalent pattern of negative epistasis in the landscape, we find that the global fitness peak is reached via four positively epistatic mutations. Combining traditional and extending recently proposed theoretical and statistical approaches, we quantify features of the global multi-allelic fitness landscape. Using subsets of this data, we demonstrate that extrapolation beyond a known part of the landscape is difficult owing to both local ruggedness and amino-acid specific epistatic hotspots, and that inference is additionally confounded by the non-random choice of mutations for experimental fitness landscapes.