Yes. If more time is needed to fully comply with the request, it can generally be granted. Asking for a great deal of company documents can generally lead to this kind of scenario.
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In normal discovery proceedures: Usually it is only necessary to call the attorney (or have your attorney call them) who represents the entitiy or person asking for the documents and ask for an extension.. If you are making a good faith attempt to produce the documents a request will typically be granted.. Try to make the extension short though..
Otherwise you can file a motion in the lawsuit which generated the discovery request
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