You should to use the RowsDetailsTemplate for the grid:
<DataGrid Grid.Row="1" Margin="4,0,4,4" AutoGenerateColumns="False" ItemsSource="{Binding SomeItemsSource}" CanUserAddRows="False" AlternatingRowBackground="#FFCED9FF" RowDetailsTemplate="{StaticResource gridDetilsTemplate}">
                <DataGrid.Columns>
                    <DataGridTextColumn Binding="{Binding SomeValue}" Header="SOME TEXT" IsReadOnly="True"/>
                    ... 
                </DataGrid.Columns>
            </DataGrid>
And the template in your parent's dictionary resources (could be in any parent dictionary resources, or also you could write the template directly in the grid):
<Window.Resources>            
        <DataTemplate x:Key="gridDetilsTemplate">
            <Border BorderBrush="Black" BorderThickness="1,0,1,1" Margin="2,0,2,2" CornerRadius="0,0,3,3" Padding="4,0,0,0">                
                <TextBlock Text="{Binding SomeValue}"/>
            </Border>
        </DataTemplate>
I think this is what you need, a grid row details. Hope works.