The integration of computational models with experimental data is a cornerstone for gaining insight into biomedical applications. However, parameter fitting procedures often require an immense availability and frequency of data that are challenging to obtain from a single source. Here, we present a novel methodology designed to integrate qualitative data from multiple laboratories, overcoming the constraints of single-lab data collection. Our method harmonizes disparate qualitative assessments-ranging from expert annotations to categorical observations-into a unified framework for parameter estimation. These qualitative constraints are represented as dynamic "qualitative windows" that capture significant trends that models must adhere to. For numerical implementation, we developed a GPU-accelerated version of differential evolution to navigate in the residuals that integrated quantitative and qualitative data. We validate our approach across a series of case studies, demonstrating significant improvements in model accuracy and parameter identifiability. This work opens new avenues for collaborative science, enabling a methodology to combine and compare findings between studies to improve our understanding of biological systems.