You don't need subinterfaces because the ISP will route those new IPs to your router anyway so the addresses don't neeed to be assigned to an interface. So lets say the 10.3.1.0/24 dept needs it's own IP -
new public IP to be used 220.127.116.11
remove 10.3.1.0 from the existing NAT acl
access-list 101 permit ip 10.3.1.0 0.0.0.255 any (note you can use a named acl if you want)
ip nat pool <-- you may want something meaningful to the dept here> 18.104.22.168 22.214.171.124 netmask 255.255.255.252
ip nat inside source list 101 pool overload
That should do it. Bear in mind when you add this config you will need to clear any existing NAT translations for the 10.3.1.x network.