Interconnections in modern systems make them vulnerable to adversarial attackers both by corrupting communication channels and compromising entire subsystems. The field of secure state estimation (SSE) aims to provide correct state estimation even when an unknown part of the measurement signals is corrupted. In this letter, we propose a solution to a novel generalized SSE problem in which full subsystems can be compromised, corrupting both the actuation and measurement signals. For a full system with p measurements, the proposed sliding mode observer (SMO)-based solution allows for up to p attack channels which can be arbitrarily distributed amongst attacks on actuation and measurement signals. This is a much larger class of attacks than considered in the existing literature. The method is demonstrated on 10 interconnected mass-spring-damper subsystems.