This work introduces a motion-planning framework for a hybrid system with general continuous dynamics to satisfy a temporal logic specification consisting of co-safety and safety components in a partially unknown environment. The framework employs a multi-layered synergistic planner to generate trajectories that satisfy the specification and adopts an iterative replanning strategy to deal with unknown obstacles. When the discovery of an obstacle renders the specification unsatisfiable, a division between the constraints in the specification is considered. The co-safety component of the specification is treated as a soft constraint, whose partial satisfaction is allowed, while the safety component is viewed as a hard constraint, whose violation is forbidden. To partially satisfy the co-safety component, inspirations are taken from indoor-robotic scenarios, and three types of (unexpressed) restrictions on the ordering of sub-tasks in the specification are considered. For each type, a partial satisfaction method is introduced, which guarantees the generation of trajectories that do not violate the safety constraints while attending to partially satisfying the co-safety requirements with respect to the chosen restriction type. The efficacy of the framework is illustrated through case studies on a hybrid car-like robot in an office environment.