Many vendors of litigation support software or services will offer to host the files and documents you collect during an investigation or lawsuit. The costs for storage can mount rapidly, even into the tens-of-thousands of dollars per month where the number of pages of documents stored reaches millions.
Some law departments, with a modicum of IT support and server capability, have taken on that storage on their own. They purchase a server and license software and store their own documents themselves. One company I have worked with followed that path. They did have to hire a service provider and obtain software for access to the database and another to ensure web access. The cost savings can be dramatic for a law department.