Is it possible to have multiple domains (each with unique child theme) on one installation?
I’m aware of WordPress’s new feature called “Network”, which allows you to have one installation for multiple sites.
Ideally each site will have it’s own child theme, or something similar.
Use the plugin WordPress MU Domain Mapping. Read the installation instructions very carefully. There is also an ebook WordPress Multisite 101 where you can read more (like migration from single site installation etc.).
You can activate themes per single site as usual. Or set the constant
WP_DEFAULT_THEME
in yourwp-config.php
depending on the host name: