Alveolar soft part sarcoma (ASPS) is a rare subtype of soft tissue sarcoma characterized by an unbalanced translocation, resulting in ASPSCR1-TFE3 fusion that transcriptionally upregulates MET expression. The European Organization for Research and Treatment of Cancer (EORTC) 90101 “CREATE” phase II trial evaluated the MET inhibitor crizotinib in ASPS patients, achieving only limited antitumor activity. We performed a comprehensive molecular analysis of ASPS tissue samples collected in this trial to identify potential biomarkers correlating with treatment outcome. A tissue microarray containing 47 ASPS cases was used for the characterization of the tumor microenvironment using multiplex immunofluorescence. DNA isolated from 34 available tumor samples was analyzed to detect recurrent gene copy number alterations (CNAs) and mutations by low-coverage whole-genome sequencing and whole-exome sequencing. Pathway enrichment analysis was used to identify diseased-associated pathways in ASPS sarcomagenesis. Kaplan–Meier estimates, Cox regression, and the Fisher’s exact test were used to correlate histopathological and molecular findings with clinical data related to crizotinib treatment, aiming to identify potential factors associated with patient outcome. Tumor microenvironment characterization showed the presence of PD-L1 and CTLA-4 in 10 and 2 tumors, respectively, and the absence of PD-1 in all specimens. Apart from CD68, other immunological markers were rarely expressed, suggesting a low level of tumor-infiltrating lymphocytes in ASPS. By CNA analysis, we detected a number of broad and focal alterations. The most common alteration was the loss of chromosomal region 1p36.32 in 44% of cases. The loss of chromosomal regions 1p36.32, 1p33, 1p22.2, and 8p was associated with shorter progression-free survival. Using whole-exome sequencing, 13 cancer-associated genes were found to be mutated in at least three cases. Pathway enrichment analysis identified genetic alterations in NOTCH signaling, chromatin organization, and SUMOylation pathways. NOTCH4 intracellular domain dysregulation was associated with poor outcome, while inactivation of the beta-catenin/TCF complex correlated with improved outcome in patients receiving crizotinib. ASPS is characterized by molecular heterogeneity. We identify genetic aberrations potentially predictive of treatment outcome during crizotinib therapy and provide additional insights into the biology of ASPS, paving the way to improve treatment approaches for this extremely rare malignancy.