Wrap something around each item in an ItemsControl

Let's say I have a collection of objects of different classes. Each class has its UserControl DataTemplated in a resource file.

Now I want to use ItemsControl to display the collection, but I want an Border or Expander around each item.

I would expect something like this to work:

<ItemsControl ItemsSource="{Binding MyObjects}">
    <ItemsControl.ItemsPanel>
        <ItemsPanelTemplate>
            <StackPanel Orientation="Horizontal"/>
        </ItemsPanelTemplate>
    </ItemsControl.ItemsPanel>
    <ItemsControl.ItemTemplate>
        <DataTemplate>
            <Border BorderBrush="Black" BorderThickness="3">
                <ContentPresenter/>
            </Border>
        </DataTemplate>
    </ItemsControl.ItemTemplate>
</ItemsControl>

But the ContentPresenter seems to pick ItemTemplate, because I get a stack overflow.

How do I get each Item's DataTemplate inside the ItemTemplate?