public class TestModel: INotifyPropertyChanged
{
  string _value1;
  public string Value1
  {
    get => _value1;
    set
    {
      _value1=value;
      OnPropertyChanged();
    }
  }

  string _value2;
  public string Value2
  {
    get => _value2;
    set
    {
      _value2=value;
      OnPropertyChanged();
    }
  }

  int _indexParam=1;
  public int IndexParam
  {
    get => _indexParam;
    set
    {
      if (value!=1 && value!=2)
        throw new ArgumentException();
      _indexParam=value;
      OnPropertyChanged();
      OnPropertyChanged(nameof(Value1));
      OnPropertyChanged(nameof(Value2));
    }
  }

  public event PropertyChangedEventHandler PropertyChanged;
  protected virtual void OnPropertyChanged([CallerMemberName] string propertyName = null)
  {
    PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
  }
}

<Window.Resources>
  <local:TestModel x:Key="TestModel" />
  <local:BoolToIntConverter x:Key="BoolToIntConverter" />
  <system:Int32 x:Key="KeyOne">1</system:Int32>
  <system:Int32 x:Key="KeyTwo">2</system:Int32>
</Window.Resources>

<Window.DataContext>
  <StaticResource ResourceKey="TestModel" />
</Window.DataContext>

<Grid>
  <Grid.RowDefinitions>
    <RowDefinition />
    <RowDefinition />
    <RowDefinition />
  </Grid.RowDefinitions>
  <CheckBox
    VerticalAlignment="Center"
    HorizontalAlignment="Center"
    IsChecked="{Binding IndexParam,
      Converter={StaticResource BoolToIntConverter},
      Mode=TwoWay,
      UpdateSourceTrigger=PropertyChanged}">
    <CheckBox.Style>
      <Style TargetType="{x:Type CheckBox}">
        <Setter Property="Content" Value="Changing Value1" />
        <Style.Triggers>
          <Trigger Property="IsChecked" Value="True">
            <Setter Property="Content" Value="Changing Value2" />
          </Trigger>
        </Style.Triggers>
      </Style>
    </CheckBox.Style>
  </CheckBox>
  <Grid
    Grid.Row="1"
    VerticalAlignment="Center">
    <TextBox Text="{Binding Value1, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}">
      <TextBox.Style>
        <Style TargetType="{x:Type TextBox}">
          <Style.Triggers>
            <DataTrigger Binding="{Binding IndexParam}" Value="{StaticResource KeyTwo}">
              <Setter Property="Visibility" Value="Collapsed" />
            </DataTrigger>
          </Style.Triggers>
        </Style>
      </TextBox.Style>
    </TextBox>
    <TextBox Text="{Binding Value2, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}">
      <TextBox.Style>
        <Style TargetType="{x:Type TextBox}">
          <Setter Property="Visibility" Value="Collapsed" />
          <Style.Triggers>
            <DataTrigger Binding="{Binding IndexParam}" Value="{StaticResource KeyTwo}">
              <Setter Property="Visibility" Value="Visible" />
            </DataTrigger>
          </Style.Triggers>
        </Style>
      </TextBox.Style>
    </TextBox>
  </Grid>
  <Grid
    Grid.Row="2"
    VerticalAlignment="Center">
    <Grid.ColumnDefinitions>
      <ColumnDefinition />
      <ColumnDefinition />
    </Grid.ColumnDefinitions>
    <TextBlock
      Text="{Binding Value1, StringFormat='Value1={0}'}" />
    <TextBlock
      Grid.Column="1"
      Text="{Binding Value2, StringFormat='Value2={0}'}" />
  </Grid>
</Grid>

public class BoolToIntConverter: IValueConverter
{
  public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
    => value is int n && n==2;

  public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
    => value is bool b && b ? 2 : 1;
}

public class BindableConverter : Freezable, IMultiValueConverter
{
  public BindableConverter()
  {
    BindingOperations.SetBinding(this, DataContextProperty, new Binding());
  }

  public object DataContext
  {
    get => GetValue(DataContextProperty);
    set => SetValue(DataContextProperty, value);
  }

  public static readonly DependencyProperty DataContextProperty =
    FrameworkElement.DataContextProperty.AddOwner(typeof (BindableConverter));

  protected override Freezable CreateInstanceCore()
  {
    throw new NotImplementedException();
  }

  public object Convert(object[] values, Type targetType, object parameter, CultureInfo culture)
  {
    if (!(DataContext is int n))
      return DependencyProperty.UnsetValue;
    return n == 1 ? values[0] : values[1];
  }

  public object[] ConvertBack(object value, Type[] targetTypes, object parameter, CultureInfo culture)
  {
    var result = new [] {Binding.DoNothing, Binding.DoNothing};
    if (!(DataContext is int n && value is string s))
      return result;
    if (n == 1)
      result[0] = value;
    else
      result[1] = value;
    return result;
  }
}

<Window.Resources>
  ............
  <local:BindableConverter
    x:Key="BindableConverter"
    DataContext="{Binding
      RelativeSource={RelativeSource Mode=FindAncestor, AncestorType={x:Type Window}},
      Path=DataContext.IndexParam}" />
</Window.Resources>
.........
<TextBox
  Grid.Row="1"
  VerticalAlignment="Center">
  <TextBox.Text>
    <MultiBinding
      Converter="{StaticResource BindableConverter}"
      Mode="TwoWay"
      UpdateSourceTrigger="PropertyChanged">
      <Binding Path="Value1" />
      <Binding Path="Value2" />
    </MultiBinding>
  </TextBox.Text>
</TextBox>

int _indexParam=1;
public int IndexParam
{
  get => _indexParam;
  set
  {
    if (value!=1 && value!=2)
      throw new ArgumentException();
    _indexParam=value;
    OnPropertyChanged();
    OnPropertyChanged(nameof(CommonValue));
  }
}

public string CommonValue
{
  get => IndexParam == 1 ? Value1 : Value2;
  set
  {
    switch(IndexParam)
    {
      case 1:
        Value1=value;
        break;
      case 2:
        Value2 = value;
        break;
      default:
        throw new ArgumentException();
    }
  }
}

<TextBox
  Grid.Row="1"
  VerticalAlignment="Center"
  Text="{Binding CommonValue, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"/>