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.