"It's actually exactly the same situation with Pred fighter, the rule simply grants an additional attack to models, that in some cases cannot legally make use of it (because they are in the second rank for example). "
The rule does not add an extra attack, that would imply that you are adding an attack on the model's profile. There would be no debate if the rule "added an attack to the profile of the entire unit." But rather it says the models "immediately make another attack". This implies the attack is made separately from the first batch. In the same way a supporting model is normally allowed to make an attack in each close combat phase, rather than just once per game.
This point is important because, supporting attacks doesn't give a time limit when it says, "can only make a single attack." Most people here are making the assumption that it means only one attack per close combat phase, but that is an assumption based on common sense. If you're doing that sort of assumption, then well, you really have no business arguing against the PF rule as intended. Because let's face it, common sense tells us supporting attackers make their additional attack. Separating out batches of dice is just plain stupid and slows the game down immensely. In a normal round you would have a batch of dice for front row attacks, a batch for front row PF attacks, and then a third for supporting attacks. And God help you if you throw poison or rerolls into the mix. The idea that this was the intent is ludicrous.
Supporting Attacks, RAW style
BRB p.49
"Of course, a warrior making a supporting attack is rather more constricted by the press of bodies than one who is face to face with his foe. To represent this, he can only ever make a single Attack, regardless of the number of Attacks on his profile, or any bonus Attacks he might otherwise be entitled to because of special rules or other unusual effects."
RAW, supporting attacking models can only ever make one attack EVER. It doesn't say "one attack per close combat phase." That's just one of those common sense things that only a jackass challenges. We know they meant, "it makes one attack at times when it is allowed to attack, rather than the number of attacks on profile." PF is allowing the model to attack again, not putting another attack on profile.
"But! That breaks the rule that supporting models can only attack once per phase!!!11"
Where does it say once per phase? It says ONE ATTACK. Period. If you're being a generous interpreter of rules as written, you will allow each supporting attacking model to make one supporting attack per game, but you're still making some degree of common sense RAI argument for that. If you're being a rules-lawyering stickler playing strictly by RAW, then what you must do is place some kind of mark on each model in your army that has EVER made a supporting attack, and be sure it never does so again. Ever. Because RAW!
My argument essentially boils down to this, you can't use RAI reasoning for how you think Supporting Attacks probably works in order to impose RAW restrictions on a separate rule. You are essentially playing Supporting Attacks as intended, and then turning around and playing with Predatory Fighter as purely RAW. I prefer to play both as they were intended.
In conclusion, here is my recommendation. Keep your BRB with you and mark page 49. If your opponent is jackass enough to insist that Supporting Attacks don't get PF rule, you pull that sucker out and point to the above quoted passage. For the rest of the game, every model who makes a supporting attack can no longer do so in subsequent phases. Explain to him/her that sometimes the rules as written bear very little in common with their intent. If you never play this person again, good riddance!