Scrum is a mindset, an approach to turning complex, chaotic problems into something that can be used. eff Sutherland and I based it on these pillars: Small, self-organizing, self-managing teams; Lean principles; and, Empiricism, using frequent inspection and adaptation to guide the work of the teams to the most successful outcome possible.
Scaled Professional Scrum is based on unit of development called a Nexus. The Nexus consists of up to 10 Scrum teams, the number depending on how well the code and design are structured, the domains understood, and the people organized.
Jeff Sutherland and I have helped hundreds of organizations scale their projects, enable their entire product development, and thread Scrum through their organizations. For sure, none of them were easy, and each had its own unique challenges.