Yes, it is possible by simply set company on project. Do not forget to set company on related tasks, timesheet,.... 

Casper Madsen,

You can move the project to another company by using the Multi Companies concept

Go to Settings -> users ,in  Extra Rights check the Multi Companies 's box

by doing this you will get the problem for feeling time-sheet of users as per their companies

here you have to allow the multiple company to user that you have defined ,which will give them to fill time-sheet according to their companies