I've just added ability to set custom condition in browse service - https://github.com/unaio/una/issues/3166

So after next UNA update you will be able to use the following service block:

array (
  'module' => 'bx_posts',
  'method' => 'browse_with_condition',
  'params' => 
  array (
    0 => 
    array (
      'mode' => 'author',
      'params' => 
      array (
        'author' => 10,
        'condition' => 
        array (
          'restriction' => 
          array (
            'public' => 
            array (
              'field' => 'allow_view_to',
              'operator' => '=',
              'value' => 3,
            ),
          ),
        ),
      ),
    ),
  ),
)