Most orchids won't bloom again on their old spikes, but Phals are a little different: the spike itself won't bloom again, but it may very well begin growing a branching spike that *will* bloom. If you don't mind looking at a "stick" for a while (the old spike), the plant itself will let you know what it's doing. If, afer a month or so, the spike dies back and turns brown and woody down to the leaves, go ahead and cut it off. If, on the other hand, it only dies back a node or two from the tip, clip off the dead part and leave the rest which should stay looking greenish-violet. It will eventually form a branch that will either bloom again or make a baby plant (called a "keiki" in the lingo) which, once it develops roots, can be cut off and potted.
Just be sure, if you do any cutting on live material, that you use either a clean razor blade or shears that have been sanitized by flame or chemical means.