Run more updates on insertion and removal

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@@ -56345,10 +56345,10 @@ interface <dfn interface>HTMLSelectedContentElement</dfn> : <span>HTMLElement</s
    any such <code>option</code> exists, otherwise null.</p></li>
 
    <li><p>If <var>option</var> is null, then run <span>clear a <code>selectedcontent</code></span>
-   given <var>insertedNode</var>.</p></li>
+   given <var>selectedcontent</var>.</p></li>
 
    <li><p>Otherwise, run <span>clone an option into a <code>selectedcontent</code></span> given
-   <var>option</var> and <var>insertedNode</var>.</p></li>
+   <var>option</var> and <var>selectedcontent</var>.</p></li>
   </ol>
 
   <p>To <dfn data-x="select-enabled-selectedcontent">get a <code>select</code>'s enabled
@@ -56407,6 +56407,31 @@ interface <dfn interface>HTMLSelectedContentElement</dfn> : <span>HTMLElement</s
    order</span>.</p></li>
   </ol>
 
+  <p>To <dfn>clear a <code>select</code>'s non-primary <code>selectedcontent</code> elements</dfn>,
+  given a <code>select</code> element <var>select</var>:</p>
+
+  <ol>
+   <li><p>Let <var>passedFirstSelectedcontent</var> be false.</p></li>
+
+   <li>
+    <p>For each <span>descendant</span> of <var>select</var> in <span>tree order</span>:</p>
+
+    <ol>
+     <li>
+      <p>If <var>descendant</var> is a <code>selectedcontent</code> element, then:</p>
+
+      <ol>
+       <li><p>If <var>passedFirstSelectedcontent</var> is false, then set
+       <var>passedFirstSelectedcontent</var> to true.</p></li>
+
+       <li><p>Otherwise, run <span>clear a <code>selectedcontent</code></span> given
+       <var>descendant</var>.</p></li>
+      </ol>
+     </li>
+    </ol>
+   </li>
+  </ol>
+
   <p>The <code>selectedcontent</code> <span>HTML element post-connection steps</span>, given
   <var>selectedcontent</var>, are:</p>
 
@@ -56441,10 +56466,39 @@ interface <dfn interface>HTMLSelectedContentElement</dfn> : <span>HTMLElement</s
     </ol>
    </li>
 
-   <li><p>If <var>nearestSelectAncestor</var> is null, then return.</p></li>
+   <li><p>If <var>nearestSelectAncestor</var> is null or <var>nearestSelectAncestor</var> has the
+   <code data-x="attr-select-multiple">multiple</code> attribute, then return.</p></li>
 
    <li><p>Run <span>update a <code>select</code>'s <code>selectedcontent</code></span> given
    <var>nearestSelectAncestor</var>.</p></li>
+
+   <li><p>Run <span>clear a <code>select</code>'s non-primary <code>selectedcontent</code>
+   elements</span> given <var>nearestSelectAncestor</var>.</p></li>
+  </ol>
+
+  <p>The <code>selectedcontent</code> <span>HTML element removing steps</span>, given
+  <var>selectedcontent</var> and <var>oldParent</var>, are:</p>
+
+  <ol>
+   <li>
+    <p>For each <var>ancestor</var> of <var>selectedcontent</var>'s <span
+    data-x="ancestor">ancestors</span> in reverse <span>tree order</span>:</p>
+
+    <ol>
+     <li><p>If <var>ancestor</var> is a <code>select</code> element, then return.</p></li>
+    </ol>
+   </li>
+
+   <li>
+    <p>For each <var>ancestor</var> of <var>oldParent</var>'s <span data-x="inclusive
+    ancestor">inclusive ancestors</span> in reverse <span>tree order</span>:</p>
+
+    <ol>
+     <li><p>If <var>ancestor</var> is a <code>select</code> element, then run <span>update a
+     <code>select</code>'s <code>selectedcontent</code></span> given <var>ancestor</var> and
+     return.</p></li>
+    </ol>
+   </li>
   </ol>