Andrews stated there is a high probability that:
Andrews encouraged his students to contribute towards the technique. One of these was a trader named Jerome Schiff. He proposed that, when price does not follow the traditional pitchfork implementation, it may follow a modified arrangement where the start point of the median line is taken to be half way between the first and second pivots.
Another variant, attributed to the Austin Financial Group  alters the first price to be the same as the third price.
Trigger (Hagopian) lines
The FPS Pitchfork tool for MetaTrader4 supports:
1. The original Andrews pitchfork.
2. The Schiff pitchfork.
3. The 50% pitchfork.
4. The Mini pitchfork.
5. All of the pitchfork variants may have hagopian (trigger) lines, inside lines and trigger lines added by manually modifying the object description.
Recommended reading (and recommended order)
1. Fisher, Greg - Using Median Lines as a Trading Tool.
2. Mikula, Patrick - The Best Trendline Methods of Alan Andrews.
3. Morge, Timothy - Trading With Median Lines.