diff --git a/kcmkwin/kwindesktop/animationsmodel.h b/kcmkwin/kwindesktop/animationsmodel.h
--- a/kcmkwin/kwindesktop/animationsmodel.h
+++ b/kcmkwin/kwindesktop/animationsmodel.h
@@ -31,6 +31,7 @@
     Q_PROPERTY(bool enabled READ enabled WRITE setEnabled NOTIFY enabledChanged)
     Q_PROPERTY(int currentIndex READ currentIndex WRITE setCurrentIndex NOTIFY currentIndexChanged)
     Q_PROPERTY(bool currentConfigurable READ currentConfigurable NOTIFY currentConfigurableChanged)
+    Q_PROPERTY(bool isImmutable READ isImmutable WRITE setIsImmutable NOTIFY isImmutableChanged)
 
 public:
     explicit AnimationsModel(QObject *parent = nullptr);
@@ -43,6 +44,9 @@
 
     bool currentConfigurable() const;
 
+    bool isImmutable() const;
+    void setIsImmutable(bool isImmutable);
+
     void load();
     void save();
     void defaults();
@@ -53,18 +57,21 @@
     void enabledChanged();
     void currentIndexChanged();
     void currentConfigurableChanged();
+    void isImmutableChanged(bool isImmutable);
 
 protected:
     bool shouldStore(const EffectData &data) const override;
 
 private:
     Status status(int row) const;
     bool modelCurrentEnabled() const;
     int modelCurrentIndex() const;
+    void loadImmutability();
 
     bool m_enabled = false;
     int m_currentIndex = -1;
     bool m_currentConfigurable = false;
+    bool m_isImmutable = false;
 
     Q_DISABLE_COPY(AnimationsModel)
 };
diff --git a/kcmkwin/kwindesktop/animationsmodel.cpp b/kcmkwin/kwindesktop/animationsmodel.cpp
--- a/kcmkwin/kwindesktop/animationsmodel.cpp
+++ b/kcmkwin/kwindesktop/animationsmodel.cpp
@@ -30,6 +30,7 @@
         [this] {
             setEnabled(modelCurrentEnabled());
             setCurrentIndex(modelCurrentIndex());
+            loadImmutability();
         }
     );
     connect(this, &AnimationsModel::currentIndexChanged, this,
@@ -78,6 +79,21 @@
     return m_currentConfigurable;
 }
 
+bool AnimationsModel::isImmutable() const
+{
+    return m_isImmutable;
+}
+
+void AnimationsModel::setIsImmutable(bool isImmutable)
+{
+    if (m_isImmutable == isImmutable) {
+        return;
+    }
+
+    m_isImmutable = isImmutable;
+    emit isImmutableChanged(m_isImmutable);
+}
+
 bool AnimationsModel::shouldStore(const EffectData &data) const
 {
     return data.untranslatedCategory.contains(
@@ -111,6 +127,21 @@
     return 0;
 }
 
+void AnimationsModel::loadImmutability()
+{
+    // Since there are many entries, consider one is enough to set immutability of
+    // switching animation option
+    KConfigGroup kwinConfig(KSharedConfig::openConfig("kwinrc"), "Plugins");
+    for (int i = 0; i < rowCount(); ++i) {
+        const QModelIndex index_ = index(i, 0);
+        const QString entryName = index_.data(ServiceNameRole).toString() + QLatin1String("Enabled");
+        if (kwinConfig.isEntryImmutable(entryName)) {
+            setIsImmutable(true);
+            break;
+        }
+    }
+}
+
 void AnimationsModel::load()
 {
     EffectsModel::load();
diff --git a/kcmkwin/kwindesktop/package/contents/ui/main.qml b/kcmkwin/kwindesktop/package/contents/ui/main.qml
--- a/kcmkwin/kwindesktop/package/contents/ui/main.qml
+++ b/kcmkwin/kwindesktop/package/contents/ui/main.qml
@@ -63,7 +63,7 @@
 
                     Layout.alignment: Qt.AlignVCenter
 
-                    text: model.display
+                    text: !!model && model.display
 
                     readOnly: true
 
@@ -76,7 +76,7 @@
 
         actions: [
             Kirigami.Action {
-                enabled: !model.IsMissing
+                enabled: !!model && !model.IsMissing
                 iconName: "edit-rename"
                 tooltip: i18nc("@info:tooltip", "Rename")
                 onTriggered: {
@@ -86,7 +86,7 @@
                 }
             },
             Kirigami.Action {
-                enabled: !model.IsMissing
+                enabled: !!model && !model.IsMissing && !kcm.isNumberImmutable
                 iconName: "edit-delete-remove"
                 tooltip: i18nc("@info:tooltip", "Remove")
                 onTriggered: kcm.desktopsModel.removeDesktop(model.Id)
@@ -106,7 +106,7 @@
 
             text: kcm.desktopsModel.error
 
-            visible: kcm.desktopsModel.error != ""
+            visible: kcm.desktopsModel.error !== ""
         }
 
         Kirigami.InlineMessage {
@@ -141,6 +141,7 @@
     footer: ColumnLayout {
         RowLayout {
             QQC2.Button {
+                enabled: !kcm.isNumberImmutable
                 text: i18nc("@action:button", "Add")
                 icon.name: "list-add"
 
@@ -157,6 +158,7 @@
                 from: 1
                 to: 20
                 editable: true
+                enabled: !kcm.isRowsImmutable
 
                 textFromValue: function(value, locale) { return i18np("1 Row", "%1 Rows", value)}
                 valueFromText: function(text, locale) { return parseInt(text, 10); }
@@ -180,6 +182,7 @@
 
             RowLayout {
                 Layout.fillWidth: true
+                enabled: !kcm.animationsModel.isImmutable
 
                 QQC2.CheckBox {
                     id: animationEnabled
diff --git a/kcmkwin/kwindesktop/virtualdesktops.h b/kcmkwin/kwindesktop/virtualdesktops.h
--- a/kcmkwin/kwindesktop/virtualdesktops.h
+++ b/kcmkwin/kwindesktop/virtualdesktops.h
@@ -37,6 +37,8 @@
     Q_PROPERTY(QAbstractItemModel* desktopsModel READ desktopsModel CONSTANT)
     Q_PROPERTY(QAbstractItemModel *animationsModel READ animationsModel CONSTANT)
     Q_PROPERTY(VirtualDesktopsSettings *virtualDesktopsSettings READ virtualDesktopsSettings CONSTANT)
+    Q_PROPERTY(bool isNumberImmutable READ isNumberImmutable CONSTANT)
+    Q_PROPERTY(bool isRowsImmutable READ isRowsImmutable CONSTANT)
 
 public:
     explicit VirtualDesktops(QObject *parent = nullptr, const QVariantList &list = QVariantList());
@@ -48,6 +50,9 @@
 
     VirtualDesktopsSettings *virtualDesktopsSettings() const;
 
+    bool isNumberImmutable() const;
+    bool isRowsImmutable() const;
+
     bool isDefaults() const override;
     bool isSaveNeeded() const override;
 
@@ -63,6 +68,8 @@
     VirtualDesktopsSettings *m_settings;
     DesktopsModel *m_desktopsModel;
     AnimationsModel *m_animationsModel;
+    bool m_isNumberImmutable = false;
+    bool m_isRowsImmutable = false;
 };
 
 }
diff --git a/kcmkwin/kwindesktop/virtualdesktops.cpp b/kcmkwin/kwindesktop/virtualdesktops.cpp
--- a/kcmkwin/kwindesktop/virtualdesktops.cpp
+++ b/kcmkwin/kwindesktop/virtualdesktops.cpp
@@ -52,6 +52,10 @@
         this, &VirtualDesktops::settingsChanged);
     connect(m_animationsModel, &AnimationsModel::currentIndexChanged,
         this, &VirtualDesktops::settingsChanged);
+
+    KConfigGroup kwinConfig(KSharedConfig::openConfig("kwinrc"), "Desktops");
+    m_isNumberImmutable = kwinConfig.isEntryImmutable("Number");
+    m_isRowsImmutable = kwinConfig.isEntryImmutable("Rows");
 }
 
 VirtualDesktops::~VirtualDesktops()
@@ -73,6 +77,16 @@
     return m_settings;
 }
 
+bool VirtualDesktops::isNumberImmutable() const
+{
+    return m_isNumberImmutable;
+}
+
+bool VirtualDesktops::isRowsImmutable() const
+{
+    return m_isRowsImmutable;
+}
+
 void VirtualDesktops::load()
 {
     ManagedConfigModule::load();