Defining mipmap size minimum?

I'd like to define the smallest size of a mipmap for a texture. Say, my texture is 1024x1024px and the smallest mipmap Unity creates should be 256x256px.

Is this possible?

The reason is the following: Unity switches textures to lower mipmaps when lowering the graphical quality via Edit > Project Settings > Quality. We're allowing our players to do that during the game, but on lower quality, the texture just looks too crappy.

Thanks!