WP_Query use for a filter with multiple Taxonomies and Terms

Try this way:

$args = array(
    'orderby'     => 'date',
    'order'       => 'DESC',
    'post_status' => 'publish'
);

if ( isset( $_POST['typefilter'] ) && $_POST['typefilter'] !== '' ) {
    $args['post_type']                = 'post_type_x';
    $args['tax_query'][0]['taxonomy'] = 'type_emp';
    $args['tax_query'][0]['field']    = 'id';
    $args['tax_query'][0]['terms']    = $_POST['typefilter'];
    $args['tax_query'][0]['operator'] = 'IN';
}

if ( $_POST['typefilter'] == '') {
    $args['post_type'] = 'post_type_x';
}

// If two or more options are selected they are sorted below
$query  = explode('&', file_get_contents("php://input"));
$params = array();

foreach( $query as $param )
{
  list($name, $value) = explode('=', $param, 2);
  $params[urldecode($name)][] = urldecode($value);
}

if( isset( $params['statusfilter'] ) && $_POST['statusfilter'] !== '' ) {
    $args['tax_query'][1]['taxonomy'] = 'status_emp';
    $args['tax_query'][1]['field']    = 'id';
    $args['tax_query'][1]['terms']    = $params['statusfilter'];
    $args['tax_query'][1]['operator'] = 'IN';
}

// for taxonomies / categories
if( isset( $_POST['cityfilter'] ) && $_POST['cityfilter'] !== '') {
    $args['tax_query'][2]['taxonomy'] = 'city_emp';
    $args['tax_query'][2]['field']    = 'id';
    $args['tax_query'][2]['terms']    = $_POST['cityfilter'];
    $args['tax_query'][2]['operator'] = 'IN';
}

$query = new WP_Query($args);

I haven’t tested it but theoretically it should work :), tell me if it works or if you need more help

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