Possible issue with SRP maybe?

You have an immediate problem here, regardless of SRP: $this->internalFoo is going to error because internalFoo is private.

Without a clearer example, it’s difficult to tell, but this doesn’t look like an SRP problem to me, however I have a few suggestions:

  1. Favour composition over inheritance:
class Child
{
    public function __construct(Parent $parent)
    {
         $this->parent = $parent;
    }

    public function foo($parameter1, $parameter2)
    {
        /* do some logic to manipulate (and basically also validate) parameters for the method internalFoo() */

        $this->parent->internalFoo([$parameter1, $this->parent->someMethod($parameter2)])

        return $this;

    }   
}
  1. Here /* do some logic to manipulate (and basically also validate) parameters for the method internalFoo() */ Why can’t internalFoo do its own validation? If this method needs to accept only valid inputs, the checks should he inside the method, imho.