Plainly we talking about using a splitter here, otherwise the answer would be one because that's all that would fit.
The answer to this is in the specification of the unit with the headphone outlet. If it is in fact a purpose-built headphone amplifier you should be able to find in the spec the lowest acceptable impedance of headphone that you can use.
Take the now-discontinued Behringer Powerplay Pro HA4400 headphone amplifier for example. The manual warns that headphones with an impedance of less than 100 ohms should not be used.
If you had two pairs of headphones of impedance 200 ohms, and a splitter, then that should be OK, but it's right on the limit of the specification. In some other headphone amplifiers this would risk distortion. In the HA4400, the output transistors would blow!
Fortunately, Behringer have now rectified this error. The Powerplay Pro-XL HA4700 can drive loads down to 8 ohms. Few headphones are available with such a low impedance. Presumably also Behringer have built in the protection circuitry that the HA4400 lacked.
So with well specified and well designed equipment, connecting headphones in parallel should not be a problem. Two questions remain however, firstly why do headphones come in different impedances?
The reasons that headphones are available in different impedances has to do with sensitivity. Other things being equal, lower impedance headphones will be louder than high impedance headphones, but they need a higher voltage output to drive them.
The second question is what would happen if you connected two pairs of headphones of different impedances to the same outlet via a splitter? The answer is that the headphones with the lower impedance would be louder, so you probably wouldn't be able to find a level that would suit both users.