In general, it involves adding additional disk drives either as individual disks in empty slots or an additional drive drawer which must be connected to the NAS controller (head) with whichever interface is used. Assuming that can be done non-disruptively, the configuration software for the NAS system is used to configure the additional capacity and create additional file systems and make them available for use to the network.
There are many variations of things that may be done but generally administrators add disk drives and change the configuration to make the extra capacity available. To learn whether the NAS system you have can do this, see if is supports non-disruptive capacity addition and configuration changes. If it's not clear from the documentation, ask the vendor's technical support.
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This was first published in May 2006