Diego Rossi
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Antagonize - Diplomacy: You fluster your enemy. For the next minute, the target takes a –2 penalty on all attacks rolls made against creatures other than you and has a 10% spell failure chance on all spells that do not target you or that have you within their area of effect.
(untyped modifier)
Intimidate - Demoralize: You can use this skill to cause an opponent to become shaken for a number of rounds. The DC of this check is equal to 10 + the target's Hit Dice + the target's Wisdom modifier. If you are successful, the target is shaken for 1 round. This duration increases by 1 round for every 5 by which you beat the DC. You can only threaten an opponent in this way if they are within 30 feet and can clearly see and hear you. Using demoralize on the same creature only extends the duration; it does not create a stronger fear condition.
Shaken: A shaken character takes a –2 penalty on attack rolls, saving throws, skill checks, and ability checks. Shaken is a less severe state of fear than frightened or panicked.
(a fear effect)
I think they stack. They are different kind of effects from different sources.
The only problem is that both effects target a single creature, not a mob.