扩展现有的类方法

Can I somehow extend existing class method from plugin? Or can I monitor output every time method get called?

There is

class greatPlugin{
...
  public function someProcess($vars){

    /* The magic */
    return $stringFromProcess;
  }
...
}

greatPlugin is called by hook inside WordPress before theme is loaded, but I need access (preferably) array of outputs generated by someProcess method. For example

$greatSubOutput = array('string1', 'string2');

or just $greatSubOutput = null; if method was not called.

The greatPlugin class is too complex to rebuild it's great work done by original dev. If I could add just some log2array feature to that function...

You can always extend the entire class, and then extend the method like so:

class loggingGreatPlugin extends greatPlugin 
{

    public function someProcess($vars) {
        $output = parent::someProcess($vars);

        $logger = new LogMe();
        $logger->log(LogLevel::INFO, $output);

        return $output;
    }
}