Corporate sustainability is considered a fundamental paradigm and solution in creating a prosperous future for organizations. However, social sustainability issues and pandemic problems from COVID-19 have affected corporations and interrupted plans for sustainable development. To date, corporate sustainability frameworks have taken a relatively narrow view of this paradigm. This study highlights serious challenges to corporate sustainability while providing a framework in an attempt to enable more sustainable business practices. To fill the gap in the literature, we have developed a framework to organize and prioritize important sustainability indicators. The first phase of the study involves the classification of 45 sub-criteria of corporate sustainability under nine main categories by using a literature review and novel Fuzzy Delphi method. The resulting categories are Corporate Governance, Product Responsibility, Transparency and Communication, Economic, Environmental, Social, Natural Environment and Climate Vulnerability, Energy Consumption along with Energy Saving, and includes Pandemic COVID-19 as a new aspect of social sustainability. Next, we applied the Fuzzy Analytical Hierarchical Process (FAHP) to help determine the weights and prioritizing the criteria and sub-criteria. The results revealed that the Pandemic, along with the Natural Environment and Climate Vulnerability, ranked higher among the main criteria category. Whereas, emergency response planning, social distances, modification of working hours, and just-in-time delivery are the most influencing sub-attributes among the 45 sub-barriers of different categories. Contributions of this study include new insights regarding corporate sustainability criteria and subcriteria, application of novel methods, and integrated framework for dimensions of corporate sustainability. This study is among the first of its kind to consider the COVID-19 pandemic as an essential category and social sustainability attribute of corporate sustainable business practices. Outcomes of this study can help assist scholars, corporations, and decision-makers in understanding sustainable development initiatives while simultaneously improving social sustainability practices.