you can definitely take more than one research design because it depends on your objective and hypothesis which hypothesis or objective will fulfill from.
You can blend different methods of data collection and analysis or various types of data in a single study, following either mixed methods research design, multimethod research design, or multimodal research design. Choosing a combination design relies on research aim and objectives and should be systematic. That being said, blending methods or data types in a research project is demanding in terms of time, effort, and money. The following references could be enlightening.
Beach, D. (2020). Multi-method research in the social sciences: A review of recent frameworks and a way forward. Government and Opposition, 55(1), 163–182. https://doi.org/10.1017/gov.2018.53
Creswell, J. W., & Plano Clark, V. L. (2018). Designing and conducting mixed methods research (3rd ed.). SAGE. https://us.sagepub.com/en-us/nam/designing-and-conducting-mixed-methods-research/book241842
Fetters, M. D., & Molina-Azorin, J. F. (2017). The journal of mixed methods researchstarts a new decade: The mixed methods research integration trilogy and its dimensions. Journal of Mixed Methods Research, 11(3), 291–307. https://doi.org/10.1177/1558689817714066
Hesse-Biber, S. N., & Johnson, R. B. (Eds.). (2015). The oxford handbook of multimethod and mixed methods research inquiry (1st ed.). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199933624.001.0001
Hiippala, T. (2017). An overview of research within the Genre and Multimodality framework. Discourse, Context & Media, 20, 276–284. https://doi.org/10.1016/j.dcm.2017.05.004
Major research design types usually include experimental, quasi-experimental, correlational, descriptive, qualitative methods. Doing 1 type of these research designs is often not easy, two types need to be done carefully, preferably with experience. It depends upon where you are in conducting research.
Doing a prospective study is more a description of the approach - is it a retrospective or prospective study of any of the above major quantitative types. The same is true of the cross-sectional approach. These are mutually compatible with each other and with the major quantitative types.