The Covid-19 pandemic caused disruptive effects for individuals, firms, and societies. In this paper, we offer insights on the major issues and challenges firms are facing in the Covid-19 pandemic, as well as their concerns for Corporate Social Responsibility (CSR) themes. To do so, we investigate large Italian firms' discussion on Twitter in the first nine months of the pandemic. We downloaded all Twitter posts from 1st of March, 2020, to 17th of November, 2020 by the accounts of the largest Italian firms, i.e. those with 250 or more employees. We then built the bipartite network of accounts and hashtags and, using an entropy-based null model as a benchmark, we projected the information contained in the network into the accounts layers, identifying a network of accounts in which a link indicates a non trivial similarity in terms of their usage of hashtags. We find that the conversation is focused around 13 communities, 10 of which include Covid-19 themes. The core of the network is formed of 5 communities, which deal with environmental sustainability, digital innovation and safety. Firms' ownership type does not seem to influence the conversation. 10 communities out of 13 mention hashtags related to CSR, with the environmental and social dimensions as the prevalent ones. Interestingly enough, the social dimension seems more relevant in the communities dealing with digital innovation and safety. However, the relevance of CSR hashtags is very small at the single message level, but with some peculiarities arising in specific communities. Overall, our paper highlights the role of network methods on Twitter data as a tool which can support managers and policy makers to design their strategies and decision making, capturing firms' emerging issues and relevant themes.