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 one or more users that belong to an organization based on user management information including organization information, user information and upper limit management information by associating with each other, said organization information, user information and upper limit management information being associated with each other in the user management information, the organization information for uniquely identifying each of the organizations, the user information for uniquely identifying each of the users each organization, the upper limit management information for managing an upper limit of an amount of process performed by each processing device for the each of the users; holding coordinate organization information to manage a plurality of groups of the organization information; specifying an organization information that belongs to a same group as a group of organization information of an organization that manages a processing device that is used by the each of the users; receiving: first specifying information that is input by a user that uses a processing device, said first specifying information specifying an organization of the user, the user information, and second specifying information that specifies an organization that manages the processing device; authenticating a login from the processing device that belongs to an organization different from that of the user when first and second conditions are met, the first condition being met when first organization information that is specified based on the first specifying information and second organization information that is specified based on the second specifying information are managed in the same group, and the second condition being met when the specified first organization information and the received user information are authenticated based on the user management information, and acquiring when a user, who is managed in the same group as a desired processing device and whose login is authenticated, makes a process request at the desired processing device, the upper limit management information from the user management information, and determining whether the process requested by the user is executable within the upper limit amount of process given to the user based on the acquired upper limit management information.