Sorry... WPF's implementation of the EventTrigger only allows one routed event.
Typically you would be firing a storyboard from a routed event. I would suggest the following compromise:
<!--Define a storyboard as a resource-->
<Storyboard x:Key="MyStoryboard1">
<!--Many properties and etc...-->
</Storyboard>
<Style.Triggers>
<EventTrigger RoutedEvent="Button.MouseEnter">
<BeginStoryboard Storyboard="{StaticResource MyStoryboard1}">
<!--Other properties/name if necessary-->
</BeginStoryboard>
</EventTrigger>
<EventTrigger RoutedEvent="Button.MouseDown">
<BeginStoryboard Storyboard="{StaticResource MyStoryboard1}">
<!--Other properties/name if necessary-->
</BeginStoryboard>
</EventTrigger>
</Style.Triggers>
The concept is to reduce duplicate code by sharing resources.
Hope this helps!