Step 1: Match the clinical intensity to the organism: ordinary acute conjunctivitis versus the aggressive hyperacute type with profuse pus.
Step 2: The garden-variety acute cases come from $Staphylococcus$ $aureus$, $Streptococcus$ $pneumoniae$ and $Haemophilus$ $influenzae$, which give moderate discharge.
Step 3: A severe, rapidly progressive, copiously discharging conjunctivitis points to $Neisseria$ $gonorrhoeae$ (or meningitidis), an organism that can invade the cornea and cause ulcerative keratitis and even perforation.
Step 4: Therefore the cause of severe conjunctivitis among the options is Neisseria.
\[\boxed{\text{Neisseria}}\]