The Holy Spirit is also God; does He proceed from Himself? Why not? You are saying the quality which makes Him proceed from the Son is the deity of the Son. Does the Son proceed from the Father and the Holy Spirit, since they are both God? Again, why not if no? Are you saying the processions orginate in the common essence? Does the Father proceed from the Son and the Holy Spirit for the same reason?
You are going to have to be a bit more clear.