Context. Core-collapse Supernovae (CC-SNe) descend from progenitors more massive than about 8 M . Because of the young age of the progenitors, the ejecta may eventually interact with the circumstellar medium (CSM) via highly energetic processes detectable in the radio, X-ray, ultraviolet (UV) and, sometimes, in the optical domains. Aims. In this paper we present ultraviolet, optical and near infrared observations of five type II SNe, namely SNe 2009dd, 2007pk, 2010aj, 1995ad, and 1996W. Together with few other SNe they form a group of moderately luminous type II events. We investigate the photometric similarities and differences among these bright objects. We also attempt to characterise them by analysing the spectral evolutions, in order to find some traces of CSM-ejecta interaction. Methods. We collected photometry and spectroscopy with several telescopes in order to construct well-sampled light curves and spectral evolutions from the photospheric to the nebular phases. Both photometry and spectroscopy indicate a degree of heterogeneity in this sample. Modelling the data of SNe 2009dd, 2010aj and 1995ad allows us to constrain the explosion parameters and the properties of the progenitor stars.