Multi template files for a content type
Sure.  You can use hook_preprocess_node() to do this, eg, something along the lines of:

function YOURTHEME_OR_MODULE_preprocess_node(&amp;$variables) {

  $node=$variables['node'];

  $foo= /* get the value of this field from $node */ ;

  $variables['theme_hook_suggestions'][] = 'node__' . $foo;

  // or....

  switch ($foo) {

    case 'FIRSTVALUE':
      $variables['theme_hook_suggestions'][] = 'node__FIRSTSOMEOTHERSTRING';
      break;

    case 'SECONDVALUE':
      // etc etc etc

  }

}


and then Drupal 7 will look for a node--WHATEVER.tpl.php.

ADDITION:

If you are wanting the PAGE itself to be different based upon this field, then you would use hook_preprocess_page() with similar logic but using page__WHATEVER instead in the theme hook suggestions and page--WHATEVER.tpl.php in the template names.