You can run multiple websites off a single IP in IIS, but you'll need to setup a separate IIS Site. It will not work as a virtual directory in your first site and correctly resolve via the second FQDN.
If you are leasing this server and only have access to your website via a control panel you will most likely not be able to do this and will need to purchase another IIS site from your vendor.
You didn't specify what access you have to the server, but if you have access (and permissions) to modify IIS then you would do the following:
Edit existing site bindings
- Open IIS Manager
- On the left hand side expand the Server node and the Sites Node
- Select your site
- Click on Bindings on the far right int he Actions section
- Select each binding and edit them one at a time
- Enter the FQDN for your first site (if this is not already
specified) in the Host Name field
- Click close when finished
Create a new Application Pool for your new site
- On the left hand side select Application Pools
- Right click on Application Pools
- Select Add Application Pool
- Enter the name of your new website
- Click OK
Create the new website
- On the left hand side select Sites
- Right click on Sites
- Select Add Website
- Enter the site name
- Select the Application Pool by clicking Select and choosing the new
Application Pool you created in the previous step
- Enter the Physical Path to your website files
- Select the IP address (the one you already have) for the Binding
- Enter the host name in Host name field
- Click OK
If you have Powershell access and would like to do it that way use the following:
Get-WebBinding -IPAddress 159.68.0.0 -Port 80 | Set-WebBinding -HostHeader www.example1.com
New-WebAppPool -Name MySite
New-Website -Name MySite -Port 80 -IPAddress 159.68.0.0 -HostHeader www.example2.com -PhysicalPath D:\Websites\www.example2.com -ApplicationPool MySite
You might be able to achieve your initial goal with URLRewrite, but it won't always work and would depend on how complicated your second website is. I wouldn't recommend this method and would do the previous steps I outlined.