Inherit/override core module
There's no inheritance for modules, but much of the functionality they provide can be altered using hooks (search this page for _alter and you'll see the ones core provides).

Specifically for items defined in hook_menu(), you can use hook_menu_alter(), e.g.

function MYMODULE_menu_alter(&amp;$items) {
  // Replace the page callback for the foo/bar path
  $items['foo/bar']['page callback'] = 'MYMODULE_some_function;
}


If I've misunderstood and you mean you literally want to inherit from a module, like subclassing a class, and just change a couple of things, then unfortunately not. Copying the module is the way to go; you'll need to change the names of all the functions so they don't collide with those in the core module, and change paths/cache keys/variables for the same reason.