Yes, this is possible by enabling the Allow Setting Page Skin option in the Site Settings and then choosing a different skin from the Skin dropdown in the Page Settings.
You can share style between skins by placing the shared CSS in a location easily accessible by all of the skins ("\Data\Style\MySharedStyles\") and then referencing those stylesheets from the style.config of each skin. For example:
<file cssvpath="/Data/Style/MySharedStyles/style-shared.css" imagebasvpath="/Data/Style/MySharedStyles/images/">none</file>
Using this method, you can have all of your style in the shared location and use only a layout.master, style.config and theme.skin in each of your skin folders.