Yes you can do this. I’ve answered a couple posts here in the forums, but I couldn’t find them when I tried to search. To get started, all you would need to do is duplicate the home.php file and change the file name to page_home.php. Then you’ll need to convert it to a template file that you will select on the page you’re using it on by adding this to the top of the file (right under the first <?php) –
// Template Name: Home Template
That will convert it to a template.
Then comes the hard part – If you add content inside any of the home widgets they’ll show up on this page, as well as the homepage. In order to separate them you could either use a multiple sidebar plugin like “Custom Sidebars” or rename all of the widgets to different labels and then register those names in your functions.php file. If you choose the plugin route, then it will allow you to use the same widget location to show different content on multiple pages.