Session variables unknown during building of menu middleware

I want my webmaster to be able to impersonate as another user. Therefore I have a form with a controller to write a session variable containing the ID he is impersonating. In my authentication middleware I check for the presence of this session variable:

class AuthenticateOnceWithBasicAuth {
  public function handle($request, Closure $next) {
    if (Session::has('simulate_as')) {
      $username = Session::get('simulate_as');
    } 
    else {
      $username = $_SERVER["REMOTE_USER"]; // fallback on single login authentication
    }
    $user = User::where('username', $username)->first();

    Auth::login($user);

    return $next($request);
  }
}

Problem is that when using the menu middleware, the session is not yet sent to the browser. Should I change something in the order of my items in kernel.php?

protected $middleware = [
  \Illuminate\Foundation\Http\Middleware\CheckForMaintenanceMode::class,
  \App\Http\Middleware\AuthenticateOnceWithBasicAuth::class,
  \App\Http\Middleware\MenuMiddleware::class,
  \Illuminate\Session\Middleware\StartSession::class,
  \Illuminate\View\Middleware\ShareErrorsFromSession::class,
];