I would use either Auto Nat or twice nat.
Auto NAT:
object network inside-server
host 192.168.1.10
nat static 2.2.2.10 service tcp 443 443
In the above example, 2.2.2.10 represents the new public IP address. It doesn't and indeed can't be configured as a secondary IP on the existing ASAs public interface. The service https is just for illustration purposes. The object 'inside-server' represents the server on the inside, using its real ip address.
The resulting output in ASDM would look something like this:
Twice NAT:
object network inside-server-public
host 2.2.2.10 <-----------------New network object corresponding to the new Public IP
object service https
service tcp destination eq https <------You may create a new service object for the services you wish to publish
nat (inside,outside) 1 source static inside-server inside-server-public service https https
The resulting output in ASDM would look something like this:
Then, create/modify the ACL to permit the desired traffic to pass:
access-list outside_access_in line 1 extended permit https any any
access-group outside_access_in in interface outside
Inbound routing for the new block will need to be handled by the modem. I believe the ASA would proxy-arp for requests to the new public address.
