Rent increase for legal successor

[Phaedrus]

My sister asked my landlord to add my name to her lease. She was informed by the landlord that he had no legal responsibility to do so (which I believe is true), but said that If I wished to take over the lease we would have to renegotiate rent. As I have been living with my sister for eight years (and informing the landlord of this fact), I am clearly the legal successor to the lease. I don't understand what negotiating would have to be done- how much can the landlord legally increase the rent if I take over the lease?
Moreover, my sister(an actress) let it slip that she's spending more time in California than before, and the landlord is demanding an ffadavit that the apartment is her sole residence. Not primary, but sole- is this right? I have gone over our lease several times now, and have found nothing that says the apartment must be the sole (or even primary) residence in order for the tenat to keep the lease.
I am getting very panicked, since there were repairs and other issues I wanted to take care of-having a legal problem with my landlord is going to make me afraid to even ask.

[Cranky Tenant]

Many Landlords are reluctant to add anyone's name to a Rent Stabilized lease because they don't want the apartment passed on from one person to another without a rent increase.

If this is the first succession the LL is not entitled to any increase beyond the normal guidelines for lease renewal. If this is the second succession, the LL is entitled to a vacancy increase plus the normal amount for lease renewal set by the Rent Guidelines Board.
DHCR Fact Sheet #30

Unless you and your sister are paying less than the maximum allowed under Rent Stabilization, the rent isn't negotiable, - unless he wants to offer you the apartment for less (not likely) Even so, that doesn't keep many Landlords from trying.