This research aims to measure the research impact of 27 private Higher Education Institutes (HEIs) in India through the lens of citations and social media. It applies data carpentry tools and techniques for gathering and formatting data from different databases. The primary bibliographic data was collected from Scopus, and the secondary data from four different databases (Dimensions.ai, Altmetric.com, Mendeley.com, and Unpaywall.org). The data is analysed in terms of coverage, associations between variables (citations vs. altmetrics), and open access advantages of altmetric. The result indicates that 18.51 % of publications from private HEIs are covered in altmetric, while 95.77 % of publications are in Mendeley. Twitter event has the most extensive coverage among altmetric data, and Dr D.Y. Patil Vidyapeeth registered with the broadest coverage in altmetric. The coverage level of altmetric data is higher for institutions focused on multidisciplinary research than medical, technical, and management institutions. The correlation results showed an almost positive between citations and altmetric mentions. Moreover, the coverage of open access publications in altmetric is considerably higher than those of non-OA articles. The Open Access Altmetric Advantages (OAAA) and Categorical Open Access Altmetric Advantages (COAAA) confirmed the open access advantages of selected institutions across altmetric events. The overall research result suggests that discipline- and institute-specific considerations are pivotal when evaluating institutions’ productivity using altmetric.