在Joe使用pinvoke和dependency属性的评论之后，我最终得到了这段代码。如果代码太长，我不应该把它都放在这里，我现在要道歉。在大小上的数学计算并不完美。WPF Actual（Height/Width）和Rect.Height/Width之间有很大的差异，可能需要一些计算才能得到你想要的确切大小。
已将其添加到MainWindow类中

[StructLayout(LayoutKind.Sequential)]
public struct RECT
{
    public int X;
    public int Y;
    public int Width;
    public int Height;
}

public enum SpecialWindowHandles
{
    HWND_TOP = 0,
    HWND_BOTTOM = 1,
    HWND_TOPMOST = -1,
    HWND_NOTOPMOST = -2
}

[DllImport("user32.dll", SetLastError = true)]
static extern bool GetWindowRect(IntPtr hWnd, ref RECT Rect);

[DllImport("user32.dll")]
[return: MarshalAs(UnmanagedType.Bool)]
static extern bool SetWindowPos(IntPtr hWnd, IntPtr hWndInsertAfter, int X, int Y, int cx, int cy, uint uFlags);

public static readonly DependencyProperty WindowHeightAnimationProperty = DependencyProperty.Register("WindowHeightAnimation", typeof(double),
                                                                                            typeof(MainWindow), new PropertyMetadata(OnWindowHeightAnimationChanged));

private static void OnWindowHeightAnimationChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
{
    var window = d as Window;

    if (window != null)
    {
        IntPtr handle = new WindowInteropHelper(window).Handle;
        var rect = new RECT();
        if (GetWindowRect(handle, ref rect))
        {
            rect.X = (int)window.Left;
            rect.Y = (int)window.Top;

            rect.Width = (int)window.ActualWidth;
            rect.Height = (int)(double)e.NewValue;  // double casting from object to double to int

            SetWindowPos(handle, new IntPtr((int)SpecialWindowHandles.HWND_TOP), rect.X, rect.Y, rect.Width, rect.Height, (uint)SWP.SHOWWINDOW);
        }
    }
}

public double WindowHeightAnimation
{
    get { return (double)GetValue(WindowHeightAnimationProperty); }
    set { SetValue(WindowHeightAnimationProperty, value); }
}

public static readonly DependencyProperty WindowWidthAnimationProperty = DependencyProperty.Register("WindowWidthAnimation", typeof(double),
                                                                                            typeof(MainWindow), new PropertyMetadata(OnWindowWidthAnimationChanged));

private static void OnWindowWidthAnimationChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
{
    var window = d as Window;

    if (window != null)
    {
        IntPtr handle = new WindowInteropHelper(window).Handle;
        var rect = new RECT();
        if (GetWindowRect(handle, ref rect))
        {
            rect.X = (int)window.Left;
            rect.Y = (int) window.Top;
            var width = (int)(double)e.NewValue;
            rect.Width = width;
            rect.Height = (int) window.ActualHeight;

            SetWindowPos(handle, new IntPtr((int)SpecialWindowHandles.HWND_TOP), rect.X, rect.Y, rect.Width, rect.Height, (uint)SWP.SHOWWINDOW);
        }
    }
}

public double WindowWidthAnimation
{
    get { return (double)GetValue(WindowWidthAnimationProperty); }
    set { SetValue(WindowWidthAnimationProperty, value); }
}

private void GrowClick(object sender, RoutedEventArgs e)
{
    this.AnimateWindowSize(Width+200, Height+200);
}

/// <summary>
/// SetWindowPos Flags
/// </summary>
public static class SWP
{
    public static readonly int
    NOSIZE = 0x0001,
    NOMOVE = 0x0002,
    NOZORDER = 0x0004,
    NOREDRAW = 0x0008,
    NOACTIVATE = 0x0010,
    DRAWFRAME = 0x0020,
    FRAMECHANGED = 0x0020,
    SHOWWINDOW = 0x0040,
    HIDEWINDOW = 0x0080,
    NOCOPYBITS = 0x0100,
    NOOWNERZORDER = 0x0200,
    NOREPOSITION = 0x0200,
    NOSENDCHANGING = 0x0400,
    DEFERERASE = 0x2000,
    ASYNCWINDOWPOS = 0x4000;
}

在OP的代码中，我相应地更改了height和width目标属性

Storyboard.SetTargetProperty(aniHeight, new PropertyPath(Window.HeightProperty));
Storyboard.SetTargetProperty(aniWidth, new PropertyPath(Window.WidthProperty));

到

Storyboard.SetTargetProperty(aniHeight, new PropertyPath(MainWindow.WindowHeightAnimationProperty));
Storyboard.SetTargetProperty(aniWidth, new PropertyPath(MainWindow.WindowWidthAnimationProperty));

原答复：
从我所发现的没有问题，你的代码。当我改变了顺序，我添加动画到故事板（sb.Children.Add）示例，我得到了高度动画没有宽度。
这使我相信，当第一个动画正在发生时，另一个动画将无效。
我所能想到的是让他们一个接一个地动画，让一个动画比另一个稍长。更长的动画将在第一个动画完成后出现。

var sb = new Storyboard { Duration = new Duration(new TimeSpan(0, 0, 0, 0, 300)) };

var aniWidth = new DoubleAnimationUsingKeyFrames();
var aniHeight = new DoubleAnimationUsingKeyFrames();

aniWidth.Duration = new Duration(new TimeSpan(0, 0, 0, 0, 300));
aniHeight.Duration = new Duration(new TimeSpan(0, 0, 0, 0, 150));

aniHeight.KeyFrames.Add(new EasingDoubleKeyFrame(target.ActualHeight, KeyTime.FromTimeSpan(new TimeSpan(0, 0, 0, 0, 00))));
aniHeight.KeyFrames.Add(new EasingDoubleKeyFrame(newHeight, KeyTime.FromTimeSpan(new TimeSpan(0, 0, 0, 0, 150))));

aniWidth.KeyFrames.Add(new EasingDoubleKeyFrame(target.ActualWidth, KeyTime.FromTimeSpan(new TimeSpan(0, 0, 0, 0, 150))));
aniWidth.KeyFrames.Add(new EasingDoubleKeyFrame(newWidth, KeyTime.FromTimeSpan(new TimeSpan(0, 0, 0, 0, 300))));

即使使用XAML故事板，我也无法同时调整窗口的高度和宽度。

对我来说，新DP的一个建议似乎有点过头了，特别是因为解决方案承认它仍然不能同时调整大小。在我的快速实验中，添加一个延迟（通过Task.Run（）），即使是1ms，也能达到最终的结果（窗口大小调整）。这个解决方案也不能同时调整大小，所以动画不像它可能的那样优雅，但它最终“工作”了。

我知道这是一个老线索，但我发现一个变通办法，似乎工作“可以接受”，至少在.net 7测试。代替动画窗口属性，设置大小的内容和定义窗口大小使用SizeToContent="WidthAndHeight"。然后动画网格大小。它不是平滑的肯定（每一帧都会导致一次重画，因为这就是windows的工作原理，我怀疑任何解决方案都无法解决这个问题），但至少它的宽度/高度是平行的。

<Window ... SizeToContent="WidthAndHeight">
    <Window.Resources>
        <Storyboard x:Key="MainStory">
            <DoubleAnimation Storyboard.TargetName="SizingGrid" Storyboard.TargetProperty="(Grid.Width)" Duration="00:00:01" To="1200"/>
            <DoubleAnimation Storyboard.TargetName="SizingGrid" Storyboard.TargetProperty="(Grid.Height)" Duration="00:00:01" To="800"/>
        </Storyboard>
    </Window.Resources>
    <Grid Name="SizingGrid" Width="640" Height="480">
        ...
    </Grid>
</Window>