Dear Brooklyn Landlord:
If your three family building is properly registered with the City as a multiple dwelling, and the last lease expired, as long as your long term tenant agrees to the rent increase, there is no formal form of notice required.
The tenancy is considered month to month and is governed by the terms and conditions of the last expired lease.
If your tenant turns down your offer will you negotiate or terminate the tenancy and start an eviction proceeding? There is some value in having a stable relationship with the tenant.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
Not unless there's an old lease (from years ago) that prescribed some other method.
I'm just 3 "helpful" answers away from a free toaster-oven! I may be guessing or not licensed in your state. No atty/client relationship exists.
They are holdover tenants so the old lease applies. Read it to what it says abour increases.
The above answer, and any follow up comments or emails is for informational purposes only and not meant as legal advice.