Help with my phalaenopsis

[angmom]

I received this phalaenopsis as a present and has had several months of blooming. Slowly the blossoms are starting to drop off and I'm faced with the question of where to cut off the spike once all the flowers are gone. As you can see by the photo there is one main spike but it branches out 3 times. If I were to cut above one of the branches would it branch out again?
Thanks for any suggestions.