A pre-schedule is a list of "executives" generated offline for a set of time-driven jobs. If in addition there exists event-driven workload competing for resources, sufficient slacks must be embedded in a valid pre-schedule. A pre-scheduler was defined in [13] with the following assumptions: the competing workload is modeled as sporadic tasks and the time-driven jobs to be pre-scheduled are independent. In this paper, the pre-scheduling problem is generalized. First, the event-driven workload is no longer limited to sporadic tasks or any specific task model. Instead, a new concept called "pre-scheduling space" is introduced so that the time-driven jobs to be pre-scheduled are inside the space, the competing event-driven workload is outside the space, and resource competition is abstracted to the space bounded by a supply function and a supply contract. Second, precedence constraints between the time-driven jobs to be pre-scheduled are allowed. The generalized pre-scheduler presented in this paper produces a valid pre-schedule if and only if one exists under the constraints of execution time bounds, valid scopes, precedence requirements and supply contract; otherwise, it returns a notice of failure. The generalized pre-scheduler runs in time polynomial to the number of time-driven jobs.