One factor related to the amount of passengers (and crew) permitted on a ship, will be a restriction, based on the number of Lifeboats/Liferafts that are on the vesse,l and the capability of those to safely accommodate all permitted personnel onboard. (Passengers + Crew).

A Passenger Ship Safety Certificate will display this statistic.

However, not fully acquainted with Maritime Law even although I have spent a fair amount of my working life onboard merchant vessels, perhaps someone else can corroborate that fact.

Malcolm