Instead of extending the home folder you could source the home directory out to an extra partition. This will also make it a lot easier to migrate to a new system without having to move the home directory.
Create a new partition and format it with a filesystem of your choice (i.e. ext4). Copy everything from your home folder to the new partition and then tell your system to mount the new partition in your home directory during startup by adding a corresponding line to /etc/fstab:
UUID=<some UID of your new partition> /home/username ext4 nodev,nosuid 0 1
Depending on the filesystem and mount options you might need to alter this line.
Edit - Ahh got ya. You really want both drives. In that case LVM could do it, but you would have to store your data somewhere while you make the partition...
sudo vgcreate vol_grp1 /dev/sda7
sudo lvcreate -n logical_vol1 vol_grp1
sudo mkfs.ext3 /dev/vol_grp1/logical_vol1
Then mount it somewhere and copy your data to it. Unmount your current home disk and mount the new VG disk in its place. After this you'll be able to extend it to the original drive with lvextend.
vgextend logical_vol1 /dev/sda?