diff --git a/src/wp-includes/html-api/class-wp-html-tag-processor.php b/src/wp-includes/html-api/class-wp-html-tag-processor.php
index 818dca6a0f..445de9ee29 100644
--- a/src/wp-includes/html-api/class-wp-html-tag-processor.php
+++ b/src/wp-includes/html-api/class-wp-html-tag-processor.php
@@ -2270,6 +2270,7 @@ class WP_HTML_Tag_Processor {
 	 *
 	 * @since 6.2.0
 	 * @since 6.2.1 Shifts the internal cursor corresponding to the applied updates.
+	 * @since 6.4.0 No longer calls subclass method `next_tag()` after updating HTML.
 	 *
 	 * @return string The processed HTML.
 	 */
@@ -2303,24 +2304,25 @@ class WP_HTML_Tag_Processor {
 		 * Rewind before the tag name starts so that it's as if the cursor didn't
 		 * move; a call to `next_tag()` will reparse the recently-updated attributes
 		 * and additional calls to modify the attributes will apply at this same
-		 * location.
+		 * location, but in order to avoid issues with subclasses that might add
+		 * behaviors to `next_tag()`, the internal methods should be called here
+		 * instead.
+		 *
+		 * It's important to note that in this specific place there will be no change
+		 * because the processor was already at a tag when this was called and it's
+		 * rewinding only to the beginning of this very tag before reprocessing it
+		 * and its attributes.
 		 *
 		 * <p>Previous HTML<em>More HTML</em></p>
-		 *                 ^  | back up by the length of the tag name plus the opening <
-		 *                 \<-/ back up by strlen("em") + 1 ==> 3
+		 *                 ↑  │ back up by the length of the tag name plus the opening <
+		 *                 └←─┘ back up by strlen("em") + 1 ==> 3
 		 */
-
-		// Store existing state so it can be restored after reparsing.
-		$previous_parsed_byte_count = $this->bytes_already_parsed;
-		$previous_query             = $this->last_query;
-
-		// Reparse attributes.
 		$this->bytes_already_parsed = $before_current_tag;
-		$this->next_tag();
-
-		// Restore previous state.
-		$this->bytes_already_parsed = $previous_parsed_byte_count;
-		$this->parse_query( $previous_query );
+		$this->parse_next_tag();
+		// Reparse the attributes.
+		while ( $this->parse_next_attribute() ) {
+			continue;
+		}
 
 		return $this->html;
 	}
diff --git a/tests/phpunit/tests/html-api/wpHtmlProcessorBreadcrumbs.php b/tests/phpunit/tests/html-api/wpHtmlProcessorBreadcrumbs.php
index 932b3ca8f2..6f8f114025 100644
--- a/tests/phpunit/tests/html-api/wpHtmlProcessorBreadcrumbs.php
+++ b/tests/phpunit/tests/html-api/wpHtmlProcessorBreadcrumbs.php
@@ -410,6 +410,53 @@ class Tests_HtmlApi_WpHtmlProcessorBreadcrumbs extends WP_UnitTestCase {
 		);
 	}
 
+	/**
+	 * Ensures that updating tag's attributes doesn't shift the current position
+	 * in the input HTML document.
+	 *
+	 * @since 6.4.0
+	 *
+	 * @ticket 59607
+	 *
+	 * @covers WP_HTML_Tag_Processor::get_updated_html
+	 */
+	public function test_remains_stable_when_editing_attributes() {
+		$p = WP_HTML_Processor::create_fragment( '<div><button>First<button><b here>Second' );
+		$p->next_tag( array( 'breadcrumbs' => array( 'BUTTON', 'B' ) ) );
+
+		$this->assertSame(
+			array( 'HTML', 'BODY', 'DIV', 'BUTTON', 'B' ),
+			$p->get_breadcrumbs(),
+			'Found the wrong nested structure at the matched tag.'
+		);
+
+		$p->set_attribute( 'a-name', 'a-value' );
+
+		$this->assertTrue(
+			$p->get_attribute( 'here' ),
+			'Should have found the B tag but could not find expected "here" attribute.'
+		);
+
+		$this->assertSame(
+			array( 'HTML', 'BODY', 'DIV', 'BUTTON', 'B' ),
+			$p->get_breadcrumbs(),
+			'Found the wrong nested structure at the matched tag.'
+		);
+
+		$p->get_updated_html();
+
+		$this->assertTrue(
+			$p->get_attribute( 'here' ),
+			'Should have stayed at the B tag but could not find expected "here" attribute.'
+		);
+
+		$this->assertSame(
+			array( 'HTML', 'BODY', 'DIV', 'BUTTON', 'B' ),
+			$p->get_breadcrumbs(),
+			'Found the wrong nested structure at the matched tag after updating attributes.'
+		);
+	}
+
 	/**
 	 * Ensures that the ability to set attributes isn't broken by the HTML Processor.
 	 *
@@ -417,7 +464,7 @@ class Tests_HtmlApi_WpHtmlProcessorBreadcrumbs extends WP_UnitTestCase {
 	 *
 	 * @ticket 58517
 	 *
-	 * @covers WP_HTML_Processor::set_attribute
+	 * @covers WP_HTML_Tag_Processor::set_attribute
 	 */
 	public function test_can_modify_attributes_after_finding_tag() {
 		$p = WP_HTML_Processor::create_fragment( '<div><figure><img><figcaption>test</figcaption></figure>' );