Have Eevee level up near a new location similar to Leafeon and Glaceon.
Have Eevee level up holding a new item similar to Weavile and Gliscor.
Have Eevee level up while another new Pokemon is present in party similar to Mantine.
Have Eevee level up if it Male/Female but not the other similar to Vespiquen.
Have Eevee level up with an open slot in party similar to Shedinja.
Have Eevee level up as Male/Female similar to Mothim and Wormadam.
Expose Eevee to a new stone similar to Gallade and Froslass.
Trade Eevee while it holds a new item similar to Electivire and Magmortar.
I can't think of a way to make Eevee evolve similar to Karrablast and Shelmet.
Sorry that it is small but the only one I could find.