Indeed. From the linked articles above:
> Because the doors to the stairwells and exits were locked – a common practice at the time to prevent workers from taking unauthorized breaks and to reduce theft – many of the workers could not escape from the burning building and jumped from the high windows.
> Various historians have also ascribed the exit doors being locked to management's wanting to keep out union organizers due to management's anti-union bias. The foreman who held the stairway door key had already escaped by another route.
> Within three minutes, the Greene Street stairway became unusable in both directions. Terrified employees crowded onto the single exterior fire escape – which city officials had allowed Asch to erect instead of the required third staircase
> The toxic smoke, heat, and the resulting human rush toward the main exit killed 100; 230 were injured and another 132 escaped uninjured.
> By this time, the nightclub's fire alarm had activated, and although there were four possible exits, most people headed for the front door through which they had entered. The ensuing crowd crush in the narrow hallway leading to that exit quickly blocked the exit completely and resulted in numerous deaths and injuries among the patrons and staff.
> Twenty-five workers were killed and 55 injured in the fire, trapped behind locked fire doors.
> The majority of those who escaped unharmed were workers in the front of the building who left through the unlocked main entrance,
It seems clear that two entrances/exists are not enough, even if there is numerous of extra emergency exists. People will, in panic, return to the point they came from, even if emergency exists are highlighted.