In a very specific situation there is a need to do address translation of both the source and destination address of a connection.
Is this possible with the asa?
Yes it's possible. Assuming you are doing it from inside to outside here's an example -
src address of host = 192.168.5.10
destination address = 22.214.171.124
You want to NAT the src address to 126.96.36.199
You want to present the destination address to the inside host as 172.16.10.1
So from the host 192.168.5.10 you would connect to 172.16.10.1. When the traffic passes through the ASA the src changes to 188.8.131.52 and the destination changes to 184.108.40.206
static (inside,outside) 220.127.116.11 192.168.5.10 netmask 255.255.255.255
static (outside,inside) 172.16.10.1 18.104.22.168 netmask 255.255.255.255