This article extends the socially responsible multiobjective problem to (i) estimating optimal portfolios via reward/risk maximization, (ii) including dependence structure between asset returns using vine copulas, and (iii) incorporating enhanced indexation utilizing cumulative zero-order stochastic dominance (CZϵSD). Applying the multiobjective optimal portfolio (MOOP) approach to a sample of EuroStoxx 50 constituents, the results show that the MOOPs provide investors with the flexibility to incorporate different objectives while investing in optimal portfolios. Including social responsibility results in lower portfolio return and economic performance, but at the same time portfolio risk, expected shortfall of portfolio returns below the benchmark, and turnover are reduced. The copula-based predictive models lead to MOOPs with higher returns and reward/risk ratios. Moreover, optimizing environmental scores leads to less risky MOOPs, while optimizing social scores results in higher average return and better risk-adjusted performance.