I'm sure you're free to charge extra based on number of people, but the question would be why take that particular fact into consideration. You're free to ask how many occupants there will be before you tell them what you want to charge for rent. If you want to ask for a larger security deposit because you anticipate greater damages, that might be way to address it.
Just personal opinion. I also think the phenomenon of monthly pet rent is weird as well, esp. when the landlord can't explain why they're charging more, e.g., that they want to spread around the cost of X, Y or Z legit extra costs to those who have pets. What costs those might be, who knows -- perhaps extra liability insurance, or extra lawn care costs to address those (not-so) pretty "urine circles". :)