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Despite a decade of reforms aimed at strengthening higher education in Peru, significant disparities persist across universities in terms of student experience, competency development, and employability outcomes. Traditional evaluation frameworks tend to analyze these dimensions separately, limiting the capacity to identify structural factors that drive quality at both the student and institutional levels. This study proposes and empirically tests a Multilevel Model of University Quality (MMUQ) that integrates individual-level data (student satisfaction, perceived competency development, career readiness indicators) with institutional-level characteristics (accreditation status, resource allocation, faculty qualifications, and research productivity). Using a sample of 18,742 students nested within 42 Peruvian universities, the study employs hierarchical linear modeling (HLM) to quantify the extent to which differences in university quality can be attributed to student-level versus institution-level determinants. Findings reveal that institutional-level factors explain 31.4% of the variance in overall university quality scores, while student-level factors explain 68.6%, demonstrating that both levels contribute significantly but asymmetrically to perceived quality. Student satisfaction with pedagogical practices and perceived development of analytical and soft skills emerge as the strongest predictors of quality at the individual level. At the institutional level, accreditation status, faculty qualifications, and library digitalization index show significant positive effects on quality indicators, while research productivity has an indirect effect mediated by competency development. The model also identifies a strong positive association between perceived competencies and early employability outcomes, suggesting that competency development is a critical mediating mechanism linking university processes to labor market results. This research offers a novel integrated approach for evaluating higher education quality in Peru, moving beyond siloed indicators toward a dynamic and multilevel understanding of how satisfaction, competency formation, and employability interact. The proposed MMUQ provides evidence-based guidelines for policymakers, accreditation agencies, and universities seeking to design interventions that simultaneously strengthen student experience, academic formation, and labor market relevance.