2D eyes on 3D character Texture problem Blender to Unity

So I have been experimenting with Blender and Unity to try and achieve a "Wind Waker Effect" with my character eyes. I plan on adding a plane in front of my characters face that will display the eyes. This plane will contain 2 separate UV maps and UV images that will animated separately.

First the eye lids will be animated similar to a sprite with the UV image snapping to the next sprite:

Now in Blender you can have one material and map 2 textures to it both with their own UV maps. So I have the second texture as the Iris and the Map can be moved around freely to have the eye look around naturally. As a bonus this eye only appears within the white space of the Eyelids:

However I know Unity can only really have 1 diffuse texture per material. In blender only one material can exist on the same plane so I cant split the textures up into their own materials. So how would I go about importing something like this into Unity?