Index: wp-includes/class-wp-term-query.php
===================================================================
--- wp-includes/class-wp-term-query.php	(revision 43547)
+++ wp-includes/class-wp-term-query.php	(working copy)
@@ -388,19 +388,48 @@
 			}
 		}
 
-		// 'term_order' is a legal sort order only when joining the relationship table.
 		$_orderby = $this->query_vars['orderby'];
-		if ( 'term_order' === $_orderby && empty( $this->query_vars['object_ids'] ) ) {
-			$_orderby = 'term_id';
+		$_orderby_array = array();
+
+		if ( is_array( $_orderby ) ) {
+			foreach ( $_orderby as $__orderby => $order ) {
+				// 'term_order' is a legal sort order only when joining the relationship table.
+				if ( 'term_order' === $__orderby && empty( $this->query_vars['object_ids'] ) ) {
+					$__orderby = 'term_id';
+				}
+				$__orderby = addslashes_gpc( urldecode( $__orderby ) );
+				$parsed = $this->parse_orderby( $__orderby );
+
+				$_orderby_array[] = $parsed . ' ' . $this->parse_order( $order );
+			}
+
+			$_orderby = implode( ', ', $_orderby_array );
+		} else {
+			$_orderby = addslashes_gpc( urldecode( $_orderby ) );
+			$order    = $this->parse_order( $this->query_vars['order'] );
+
+			foreach ( explode( ' ', $_orderby ) as $i => $__orderby ) {
+				// 'term_order' is a legal sort order only when joining the relationship table.
+				if ( 'term_order' === $__orderby && empty( $this->query_vars['object_ids'] ) ) {
+					$__orderby = 'term_id';
+				}
+				$parsed = $this->parse_orderby( $__orderby );
+				// Only allow certain values for safety.
+				if ( ! $parsed ) {
+					continue;
+				}
+
+				$_orderby_array[] = $parsed . ' ' . $order;
+			}
+			$_orderby = implode( ', ', $_orderby_array );
 		}
-		$orderby = $this->parse_orderby( $_orderby );
 
-		if ( $orderby ) {
-			$orderby = "ORDER BY $orderby";
+		$orderby = '';
+		if ( $_orderby ) {
+			$orderby = "ORDER BY $_orderby";
+			$order   = '';
 		}
 
-		$order = $this->parse_order( $this->query_vars['order'] );
-
 		if ( $taxonomies ) {
 			$this->sql_clauses['where']['taxonomy'] = "tt.taxonomy IN ('" . implode( "', '", array_map( 'esc_sql', $taxonomies ) ) . "')";
 		}