InCites is a citation-based evaluation tool for academic and government administrators to analyze institutional productivity and benchmark output against peers and aspirational peers in a national or international context.
The altmetrics of the group outputs would have to be collected manually from all the places where these are available. A quick way to keep track of these would be through subscription to PlumAnalytics.
Plum Analytics tracks more than 20 different types of artifacts, including journal articles, books, videos, presentations, conference proceedings, datasets, source code, cases, and more. Metrics are captured and correlated at the group / collection level (e.g., lab, department, museum, journal, etc.). It is a product oriented toward universities and other research institutions.