Parameter synthesis for Collective Adaptive Systems (CAS) is computationally intensive, often rendering the analysis of large-scale stochastic models impractical. This paper addresses this challenge by introducing a parameter synthesis framework integrated into the Sibilla tool. Our approach utilises machine learning surrogate models to reduce computational overhead, enabling efficient exploration of complex parameter spaces. The framework supports various synthesis tasks, including optimal feasibility, and introduces a new technique: the Variant Model Adjustment approach. This technique allows for systematic comparison and fine-tuning of model variants while adhering to specified temporal logic properties. Several case studies are provided to demonstrate the effectiveness of the framework in identifying optimal parameter configurations.