You can place more than one control into the LayoutPanel.Content property. Just wrap your buttons into panel:
<dxdo:LayoutPanel ... >
<StackPanel Orientation="Vertical">
<Button x:Name="button1" ... />
<Button x:Name="button2" ... />
</StackPanel>
</dxdo:LayoutPanel>
Related example: How to build a layout of controls within LayoutPanels