If you want to get technical, you can have a total of 64 different combinations of eeveelution ships (not counting Eevee and counting if you can ship the eeveelution with another one of the same eeveelution)
Counting Eevee you have a total of 81 possible ships. That is if you can ship the eeveelutions (and Eevee now) with another of the same eeveelution (or another Eevee if Eevee)