The short answer is no. The ControlTemplate is essentially a black box, at least where XAML is concerned (there are ways to dig down the visual tree in code).
When you say you "can't use TemplateBinding", why not? If you just don't have enough available properties that can be fixed by creating some attached properties for the values you want to pass through. This is assuming you're templating a control that you can't change, otherwise you can just add new dependency properties.
Attached property:
public static class CustomProps
{
public static readonly DependencyProperty MyNewBrushProperty = DependencyProperty.RegisterAttached(
"MyNewBrush",
typeof(Brush),
typeof(CustomProps),
new UIPropertyMetadata(Brushes.Green));
public static Brush GetMyNewBrush(DependencyObject target)
{
return (Brush)target.GetValue(MyNewBrushProperty);
}
public static void SetMyNewBrush(DependencyObject target, Brush value)
{
target.SetValue(MyNewBrushProperty, value);
}
}
And usage in Style and Template:
<Style TargetType="{x:Type Button}">
<Setter Property="local:CustomProps.MyNewBrush" Value="Red" />
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type Button}">
<Border Background="{Binding RelativeSource={RelativeSource TemplatedParent}, Path=(local:CustomProps.MyNewBrush)}">
<ContentPresenter/>
</Border>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
Using this method also still allows overriding values on individual instances.