The article continues the discussion of pilot study results concerning the specifics of university teachers' support for the idea of Open Science and is devoted to the main types of their engagement in data exchange. For this purpose, we described characteristics, subcharacteristics of engagement, and their indicators; classified the findings, conducted the step-by-step selection of engagement profiles with their further ranking according to the level of engagement, and grouped the types of engagement into common and distinctive ones. The determined types (intense, moderate, selective, and quasi) embrace all the identified relationships between various levels of engagement in empirical data exchange, namely: the shaped intention to share empirical data, the consistent application of its methods, and conscious assistance to it. The main types of engagement characterize teachers' intentions to disseminate empirical data and the possibility of such data reuse by other researchers. The findings can be valuable for the management of higher educational establishments, as it allows to evaluate teachers' readiness to disseminate the collected ED and to give permission for their reuse by other researchers. In general, the conducted research adds an important nuance to the implementation of institutional policies of research management with the purpose of promoting Open Science.