There isn't any problem for your new configuration.
I don't know what's ur configuration and ur strategy/policy but you can configure as one of the below :
- configure new host in IIS as same IP address (by using "host header name" in IIS at advance configuration)
- add new public IP address to host and permit it at PIX also add it to NAT 0
- add new private IP address to host and map it with public address (static nat)