We investigate the behavior of a standard multi-agent system (the Schelling's segregation model) when a fraction f of agents are frozen (or "pinned''). We consider cases where the frozen agents are uniformly distributed across the system, and cases where they are grouped together either (i) outside a circular region or (ii) inside an annulus. We find that these lead to different consequences on the long-time average contact density in the system. Different transitions between segregated and mixed phases can be then investigated with the variation of the control parameters of the system.