Modern applications are increasingly driven by Machine Learning (ML) models whose non-deterministic behavior is affecting the entire application life cycle from design to operation. The pervasive adoption of ML is urgently calling for approaches that guarantee a stable non-functional behavior of ML-based applications over time and across model changes. To this aim, non-functional properties of ML models, such as privacy, confidentiality, fairness, and explainability, must be monitored, verified, and maintained. Existing approaches mostly focus on i) implementing solutions for classifier selection according to the functional behavior of ML models, ii) finding new algorithmic solutions, such as continuous re-training. In this paper, we propose a multi-model approach that aims to guarantee a stable non-functional behavior of ML-based applications. An architectural and methodological approach is provided to compare multiple ML models showing similar non-functional properties and select the model supporting stable non-functional behavior over time according to (dynamic and unpredictable) contextual changes. Our approach goes beyond the state of the art by providing a solution that continuously guarantees a stable non-functional behavior of ML-based applications, is ML algorithm-agnostic, and is driven by non-functional properties assessed on the ML models themselves. It consists of a two-step process working during application operation, where model assessment verifies non-functional properties of ML models trained and selected at development time, and model substitution guarantees continuous and stable support of non-functional properties. We experimentally evaluate our solution in a real-world scenario focusing on non-functional property fairness.