The convergence of technology and human creativity in Society 5.0 demands innovative approaches to addressing complex scientific challenges across diverse domains, making cohesive experimentation essential. The growing complexity, diversity, and scale of data, combined with the need for interdisciplinary exploration and knowledge discovery, present significant challenges. Computational scientific experiments leverage various methods such as data acquisition, preprocessing, analysis, and visualization to simulate and understand intricate phenomena. However, existing interactive environments (e.g., Jupyter Notebook, Google Colab), collaborative groupware systems (e.g., Co-Taverna, iPlant Collaborative), and scientific workflow management systems (e.g., Galaxy, Kepler) often fall short in providing the automation, scalability, and reproducibility required for scientific experimentation. Additionally, they lack the usability and flexibility necessary to accommodate varying skill levels among researchers and support effective collaboration across domains. This paper introduces a collaborative framework designed to support cross-domain computational scientific experiments, fostering the automation of complex operations, intuitive workflow composition, seamless collaboration among researchers, comprehensive data and process lineage management, and integration of data, tools, and experiments. This approach allows domain experts to focus on scientific discovery rather than technical complexities. This study outlines the framework's architecture and key features, discussing the challenges it addresses in the context of Society 5.0. As a proof-of-concept, we developed a prototype workflow management system for code clone analysis, bioinformatics, image processing, and machine learning by integrating tools and services from their respective domains. Our proof-of-concept study demonstrates the framework's feasibility for collaborative cross-domain workflow creation. Additionally, an expert opinion study evaluates its flexibility in tool integration using NASA-TLX. The results demonstrate its effectiveness in facilitating cross-domain scientific experimentation, aligning with the principles of Society 5.0, and fostering innovation and knowledge discovery across diverse scientific domains. Two virtual machines hosting the prototype are available for experimentation at https://cdanalytics.usask.ca and https://swanalytics.usask.ca.