Is it possible to set different domains on one website name in Magento 1.9?
I want to have it like this: 
Is it even possible to set this in store level?
EDIT: I also did the costumisation in index.php file
if(stripos($http_host, 'mywebsite.de') !== false){ $mageRunCode = "mywebsite"; $mageRunType = "website"; }elseif(stripos($http_host, 'mywebsite.com') !== false){ $mageRunCode = "mywebsite"; $mageRunType = "website"; } and set the Base URL on different Current Configuration Scopes.
Yes, you just need to create a default store and view to each one.
You can Manage your stores like that on System > Manage Stores.
You will need to change the scope to define the base URL like that image below.
Some devs change the index.php like that below.
But the better way to handle switching the run code and run type is to use your Apache or Nginx configuration on the Virtual Host instead of modifying a "core" file (index.php).
/* Store or website code */ $mageRunCode = isset($_SERVER['MAGE_RUN_CODE']) ? $_SERVER['MAGE_RUN_CODE'] : ''; /* Run store or run website */ $mageRunType = isset($_SERVER['MAGE_RUN_TYPE']) ? $_SERVER['MAGE_RUN_TYPE'] : 'store'; switch($_SERVER['SERVER_NAME']) { case "www.store2.com": case "store2.com": $mageRunCode="base2"; $mageRunType="website"; break; default: $mageRunCode="base"; $mageRunType="website"; break; } 
In System -> Manage Stores you can create Website, stores and stores views.
Create Website: mywebsite, Create Store: mywebsite.de and mywebsite.com, Create Store View: English, French and German for each stores.
In System -> Configuration choose Current Configuration Scope and set the settings Base Url of each domain for Secure or Unsecure in the Web tab
