Resistance towards cancer treatment represents a major clinical obstacle, preventing cure of cancer patients. To gain mechanistic insights, we developed a model for acquired resistance to chemotherapy by treating mice carrying patient derived xenografts (PDX) of acute lymphoblastic leukemia with widely-used cytotoxic drugs for 18 consecutive weeks. In two distinct PDX samples, tumors initially responded to treatment, until stable disease and eventually tumor re-growth evolved under therapy, at highly similar kinetics between replicate mice. Notably, replicate tumors developed different mutations in TP53 and individual sets of chromosomal alterations, suggesting independent parallel clonal evolution rather than selection, driven by a combination of stochastic and deterministic processes. Transcriptome and proteome showed shared dysregulations between replicate tumors providing putative targets to overcome resistance. In vivo CRISPR/Cas9 dropout screens in PDX revealed broad dependency on BCL2, BRIP1 and COPS2. Accordingly, venetoclax re-sensitized derivative tumors towards chemotherapy, despite genomic heterogeneity, demonstrating direct translatability of the approach. Hence, despite the presence of multiple resistance-associated genomic alterations, effective rescue treatment for polychemotherapy-resistant tumors can be identified using functional testing in preclinical models.