What you meant: two owner's blocks, or an alternative of default?

One that is similar to the structurer of the original owner_block but with links that I populate it with and not elgg.

Just register plugin hook for it:

elgg_register_plugin_hook_handler('register', 'menu:owner_block', 'my_owner_block_menu');

Then add a menu item to the user/group ownerblock:

function my_owner_block_menu($hook, $type, $return, $params) {
    if (elgg_instanceof($params['entity'], 'user')) {
        $url = "your-url-here";
        $item = new ElggMenuItem('your-name', elgg_echo('your-name'), $url);
        $return[] = $item;
    }

    else {
            $url = "your-url-here-for-group";
           $item = new ElggMenuItem('your-name-for-group', elgg_echo('your-name-for-group'), $url);
            $return[] = $item;
    }

    return $return;
}

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