A special-purpose appliance (SPA) works in conjunction with a server farm consisting of multiple caching server appliances (CSAs) to supervise a local storage medium (i.e., a shared cache) that is accessible by all the CSAs for storing at least some of the remote objects such as web pages and their embedded objects and/or streaming media objects that have been and/or will be served by one or more of the CSAs to its respective clients. The SPA preferably also determines when to prefetch remote objects such as web pages and their embedded objects and/or streaming media objects that are not currently stored in the shared cache, but which the SPA has determined are likely to be requested in the future by one or more of the CSAs one behalf of one or more of the CSA's respective clients. In that regard, the SPA (and/or PSA) does not merely monitor the file requests from each CSA to the remote servers, but rather monitors and aggregates the individual requests from each client to its respective CSA, for example, by monitoring the access logs of each CSA and using that data to decide what to prefetch into the shared cache from the remote server or servers, what is still of value and needs to be updated, and what is no longer of value and can be replaced. What it prefetches can be based, for example, on links present in an already requested web page, on patterns of recent accesses to web pages and streaming media objects, on user profiles, and on past trends.