If you set the KeepDropDownOpen property of RadMultiColumnComboBox to False, clicking outside of the control should close the popup showing the dropdown content. This stops working after you drag a row from the GridView outside of the dropdown. For example, the drop can happen outside of the RadMultiColumnComboBox control or on its text input and drop down button area.

To resolve this, you can subscribe to the PreviewMouseLeftButtonUp event of RadMultiColumnComboBox and capture the mouse when needed.

this.mccb.AddHandler(RadMultiColumnComboBox.PreviewMouseLeftButtonUpEvent, new MouseButtonEventHandler(Mccb_MouseLeftButtonUp), true);
//---------------
private void Mccb_MouseLeftButtonUp(object sender, MouseButtonEventArgs e)
{
	var button = Mouse.DirectlyOver as RadDropDownButton;
	if (this.mccb.IsDropDownOpen && button != null && button.TemplatedParent is RadMultiColumnComboBox)
	{
		Dispatcher.BeginInvoke(new Action(() => { button.CaptureMouse(); }));
	}
}