This article proposes multiple multi-domain solutions to deploy private SG networks for vertical industries. Different models of deploying SG private networks are presented, covering deployment on local premises as well as their interconnection with public networks of mobile network operators. Building on a set of industry verticals (comprising Industry 4.0, Transportation and Energy) different deployment models are analyzed and the proposed multi-domain solutions are applied. These solutions are implemented and validated through two proof-of-concept prototypes integrating a SG private network platform (5Growth platform) with public ones. These solutions are being implemented in three vertical pilots conducted with real industry verticals. The obtained results demonstrated both the feasibility and benefits of the proposed solutions.