1. A method, with a hybrid server system comprising a server system and at least one accelerator system, for supporting multiple users in an out-of-core processing environment, the method comprising: partitioning, with at least one processor, at least one accelerator system in a plurality of accelerator systems into a plurality of virtualized accelerator systems; configuring a private client cache on each virtualized accelerator system in the plurality of virtualized accelerator systems, wherein the private client cache of each virtualized accelerator system stores data that is one of accessible by only the private client cache and accessible by other private client caches associated with a common data set; and assigning each user in a plurality of users to a virtualized accelerator system from the plurality of virtualized accelerator systems.