Sorry ... The WPF implementation of EventTrigger only allows one routable event.
Usually you start a storyboard from a routed event. I would suggest the following tradeoff:
<Storyboard x:Key="MyStoryboard1">
</Storyboard>
<Style.Triggers>
<EventTrigger RoutedEvent="Button.MouseEnter">
<BeginStoryboard Storyboard="{StaticResource MyStoryboard1}">
</BeginStoryboard>
</EventTrigger>
<EventTrigger RoutedEvent="Button.MouseDown">
<BeginStoryboard Storyboard="{StaticResource MyStoryboard1}">
</BeginStoryboard>
</EventTrigger>
</Style.Triggers>
.
, !