Harvard Data Commons (HDC) is a university-wide initiative at Harvard University to support the lifecycle of research at Harvard. The goal of the HDC is to improve research data's integrity, provenance, and reproducibility. To accomplish this goal, the HDC team has been working on automating the flow of research data from research computing environments to management, publication, discovery, and preservation environments, leading to improved researcher experience. The project's initial phase builds a proof of concept or "Harvard Data Commons Minimum Viable Product (MVP)" to connect key systems in the research data lifecycle. In addition, the Harvard Dataverse repository provides a free platform for researchers inside and outside the Harvard community to share research data as a dataset or a dataverse collection (a collection of datasets). One of the main objectives of HDC is to improve the reproducibility of research data by supporting computational workflows on the Harvard Dataverse repository. In this lightning talk, we report our progress on enhancing the Harvard Dataverse repository to support FAIR (findability, accessibility, interoperability, and reusability) computational workflows and the challenges in this area. Considering a data-driven analysis lifecycle, researchers produce different products during the whole process. These products could be peer-reviewed journal publications, curated datasets, different kinds of plots, graphs and maps, or software. Researchers design computational workflows to compose and execute a series of analysis or data manipulation steps to produce these products. Researchers could define computational workflows using workflow-specific standards/languages such as Common Workflow Language (CWL) or defined in ad-hoc scripts and notebooks such as Python, shell script, Makefile, Jupyter Notebook, or R Notebook. We report on the challenges and progress of sharing computational workflows in the Harvard Dataverse repository from allowing workflow-specific search queries in the UI to incorporating adequate metadata and runtime environments. We also present our future plans for supporting the computational workflows beyond the MVP, which would include developments like automatic tests in Dataverse and integrations with third-party workflow tools.