I thought about this and I came up with a different solution.  Assuming your plugin has a field called "class" in the XML.  

    $app = JFactory::getApplication();
    $appParams = $app->getParams();
            
    $class = "";
    if ($this->params['class'])
    {
        $class = $this->params['class'];
    }
            
    $pageClass = $appParams['pageclass_sfx'];
    if(!empty($pageClass)) 
    {
        $class = " " . $this->params['class'];
    }
    else 
    {
        $class = $this->params['class'];
    }
    $pageClass = $pageClass . $class;
    $app->setParams($pageClass);

As the menu/page class is already added to the body we can just concatenate ur new class