Am I able to have one copy of OpenX which uses different settings for different domains?

Yes, with 2.4 you are able to have seperate configuration files for different domain names.

In the openx/var folder will be your main www.example.com.conf.php configuration file.

If using 2.4.2 and above, you will also have a default.conf.php file which has the content:
realConfig=www.example.com

This means that any time you load the OpenX files from a domain which is not www.example.com, it will use the www.example.com.conf.php config file by default.

If you wish for a domain to use a different config file, you can create a file called 'test.example.com' or 'ads.example2.net'
This will let you define seperate settings to use for this domain. You can either take a complete copy of the main config file, edit the settings as needed and place the content in test.example.com.conf.php, or you can tell it to use a default config file except for a few settings. To do this, follow default.conf.php's example and use:

realConfig=www.example.com
[database]
name=openads_2024
[webpath]
admin=test.example.com/admin
delivery=test.example.com/delivery

This will use all values from the defined 'realConfig' except for ones which you define.
Note: realConfig uses only the domain name, do not place 'conf.php' after the domain
Note 2: You must use a [heading] for the settings to take affect. Any setting under the wrong heading or without a heading will not be used. Note the use of [database] and [webpath]