New Jersey allows for non-refundable pet deposits. The security deposit, in total, cannot exceed one and a half times the monthly rent; however, the most additional security money that a landlord can get in any one year is 10 percent of the current deposit. So, for example, if your current security deposit is $100, the most the landlord could get from you for additional security is $10.
And, yes, the landlord can charge additional rent.
You should also check with your city or township as sometimes they have additional rules regarding leases and security deposits.