My landlord is trying to charge for additional tenants.

If your unit is rent controlled and your lease does not say the number of tenants that can live with you, this is an illegal rent increase (see “Rent Increase Basics”). If you have Rent Control and your landlord tries to charge for an additional tenant, you can file a petition at the Rental Adjustment Program for an illegal rent increase to have a hearing on the issue.
If your lease specifically limits how many people can live in the unit, going over that limit is a material violation of the lease. It could be a Just Cause for eviction. You may receive a 3-day notice to perform covenant or quit as the start of this process.

If a tenant adds new occupants after the start of the tenancy (per the lease), the landlord can petition the Rent Board for a 5% rent increase for each new occupant (not including the CPI increase). This increase does not apply to the (biological, adopted, or foster) child, parent, grandparent, spouse, or registered domestic partner of any current tenant or a caretaker needed due to a disability. The increase goes away if the amount of occupants decreases.