Don't worry about it.
Make the view as high as the base text field and button, something like 32px I guess.
On the root container, add a overflow: visible style.
Then make the options panel where ever you want, outside of the view's boundaries.
When you place your dropdown in a view, check the useDefaultViewHeight property, make sure the embedded view is the right height (32px), and add the overflow: visible property here as well.
Make sure it's on top of other components by clicking 
or setting a z-index style.
That's it.
I'm trying to figure out if there's a way to make things simpler, maybe through css, but it's already quite simple.