In recent years, global events have redefined working life, stimulating new organizational models. This work focuses on job crafting, which is considered the way to improve the relationship between some organizational variables and other individual variables such as organizational identification and satisfaction with communication, both of which are crucial to achieving sustainable levels of well-being. The study examines the role of latent constructs that can promote adaptive responses as well as their relations. In particular, we focus on organizational identification in promoting adaptive responses, including the increase in structural resources, the increase in challenging demands, and the increase in social resources as adaptive strategies to improve satisfaction with communication. The analysis is carried out using robust statistical techniques that are suited to the study of causal relations between abstract constructs. Specifically, after Confirmatory Composite Analysis (CCA-PLS) to evaluate the quality of the data collected, a higher order mediation model, based on partial least squares structural equation modeling (PLS-SEM), was performed to test the mediation role of the job crafting. In addition, we prioritize such latent constructs using importance–performance map analysis (IPMA) to evaluate the relevance and performance of each construct of this model. The results show a relationship between organizational identification, corresponding to a high sense of belonging, and communication satisfaction at all levels through the mediation of job crafting.