When using GNU coreutils
df, get in the habit of filtering by file system type:
df -t xfs -h. Or maybe you are using ext4 or other file systems. This ignores in memory types that are not permanent storage, like tmpfs.
Create new disks (EBS volumes in the case of AWS), create LVM volumes and file systems on them. Then migrate onto the new mount points (
/srv or somewhere under
/var perhaps) by copying data. You can then do neat tricks like booting an image with upgraded software, then swing the existing disk over to the new instance.
Or, you could expand the existing disk and the file system on it. However, that ties your data to your operating system volume.