1. A process management system comprising: an information processing apparatus connected to a plurality of networks each of which is provided in respective one of organizations to which a plurality of users belong and having a processing device to be used by the users, each organization belonging to one of a plurality of groups, wherein the information processing apparatus includes a computer that executes a program to perform a managing process to manage a process performed by the processing devices in the networks, the managing process including: managing user management information including organization information, user information and upper limit management information by associating with each other, the organization information for uniquely identifying each of the organizations, the user information for uniquely identifying each user of each organization, the upper limit management information for managing an upper limit of an amount of process performed by each processing device for each user; managing coordinate organization information to manage a plurality of groups of the organization information; and managing a process performed by the processing devices by acquiring, when one of the users managed by organization information managed in one of the groups of the organization information makes a process request, the upper limit management information associated with the organization information and the user information of the user who makes the process request, from a desired one of the processing devices which is managed by the organization information of the one of the groups of the organization information, and determining whether the process requested by the one of the users is executable within the upper limit amount of process given to the one of the users based on the acquired upper limit management information, wherein the managing a process performed by the processing device includes determining to perform, when the process requested by the one of the users is determined to be executable, the process requested by the one of the users.