Landlord adding fees mid-lease

Location: central NY

We just moved in to our apartment (literally a month and a half ago) and our landlord is now trying to add a pet fee. We signed a pet addendum stating that we owed a one time pet fee (which was paid). Now they are staying they can change the rules and add more fees. There is a clause saying they can modify pet rules as per section 11(lists things like no pets in common areas, no tieing pets up outside, etc), but the pet rules deal exclusively with pet conduct, not fees and payments. I'm trying to fight it, saying that adding a fee would be a change of terms which is illegal mid lease- and that rules and fees are very different. Do I actually have backing here?