Bleed Rules:
A creature that is taking bleed damage takes the listed amount of damage at the beginning of its turn.
Bleeding can be stopped by a DC 15 heal check or through the application of any spell that cures hit point damage (even if the bleed is ability damage). Some bleed effects cause ability damage or even ability drain.
Bleed effects do not stack with each other unless they deal different kinds of damage. When two or more bleed effects deal the same kind of damage, take the worse effect. In this case, ability drain is worse than ability damage.
It's a little vague, but does this refer to ANY type of damage, such as slashing or piercing, or does it refer to bleed types such as HP, STR, CON, etc.
For example, my character uses two obsidian daggers to deal damage to an opponent, then breaks them with Splintering Weapon to cause bleed damage. As long as one dagger did damage with slashing and one with piercing, I'm pretty certain that the wording allows for a total of 2d4 bleed after both have connected (The same is true if they both did the same type of damage), but would the bleed per round total to 2d4 if one dagger did piercing and the other slashing?