A method, hybrid server system, and computer program product, support multiple users in an out-of-core processing environment. At least one accelerator system in a plurality of accelerator systems is partitioned into a plurality of virtualized accelerator systems. A private client cache is configured on each virtualized accelerator system in the plurality of virtualized accelerator systems. 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. Each user in a plurality of users is assigned to a virtualized accelerator system from the plurality of virtualized accelerator systems.