Depending on how they are configured currently, it might be possible to do this without any downtime.
For example, if the files are stored on a filesystem that’s on an LVM logical volume (LV), you can use
pvmove to move the volume to another device even while the filesystem is still in use.
If you have a second physical disk you can create a degraded RAID1 (mirror) on it with
pvcreate on the mirror device,
vgextend to add it to the LVM volume group,
pvmove the volume into the degraded mirror,
vgreduce the unused PV out of the volume group, then add the device underlying the old PV as the other side of the new mirror.
Note that this only works if the existing LV doesn’t use all of the available space on the underlying device, or it won’t fit into the mirror since a small amount of space is taken for the md-raid metadata.