Yes, it is possible, but there is no free extension for such a mighty task.
I have used AlterBrains MightySites extension before, in various Case Scenarios, with a great success.
MightySites is Joomla! multisites manager and allows you to have multiple sites running in single hosting account and share database data between different Joomla! sites, ...
There is already a simple solution that exists to achieve your aims.
If you install the Fabrik extension you can then add a new database connection within the component admin settings.
Using Fabrik you can then display and update fields and data from different databases within the same forms.
I think this is not the explanation wanted for the user, but it's possible he needs to populate the information of his master website with a plugin system to the two databases.
If you are going to implement the code by using overrides and custom components, you just have to use, for example, this simple guide to obtain information from the other ...
This question has been asked again in this website in various forms. Here is a list of relative questions with answers to your question.
Multiple website managment with Joomla?
2 domains, 2 templates one cms with same content
How to update an online website?
Mass Joomla sites Updates / Maintenance
Single source many Joomla sites on a server. How could ...
EUREKA !!!! the solution:
When Joomla is installed it has SEF-URL (search engine friendly - URL) enabled. And don't ask me why but that caused the JCE not to function in the redirected sites.
So disabling "search engine friendly" URL in Global Configuration restored JCE's Function.
Thanks to the "Hyde-design" page that put me on the right track.
That sounds like a great idea for a plugin. You could have a single site mapped to multiple domain names and let the plugin assign the template based on the domain used to visit the site. Configuration could be as easy as adding a single entry - domain=template. As many domains as you like.
That would be super easy to write too...two or three hours tops ...
I have achieved that using Multi-Sites extensions. I have tried the Mighty-Sites and Joomla Multi-Sites.
Both can be configured to share database content - although Multi-sites will require additional plugin to share Joomla articles.
I also trust Neil's opinion about the Virtual Domains, although I have never tried that extension - I have seen him speaking ...
It might be clearer if you explain how you have set up 2 domains and 2 templates with one Joomla installation.
In any case, you should be able to set up separate menu options that point to the same article and assign the relevant templates in the template settings.
It may be easier to set this up using a multi site extension such as Virtual Domains or ...