To increase or decrease the amount being withheld for state taxes because every year you are out of balance, then always go to the state version of the w-4.
There are generally worksheets that help the situation when married or if you have multiple jobs or both.
For New York state the [IT-2104 Instructions] are quite complex and there have been changes:
Changes effective beginning 2022
Form IT-2104 has been revised for tax year 2022. The worksheet and the
charts below, used to compute withholding allowances or to enter an
additional dollar amount on line 3, 4, or 5, have been revised. If you
previously filed a Form IT-2104 and used the worksheet or charts, you
should complete a new 2023 Form IT-2104 and give it to your employer.
The section " Who should file this form" has a long list that includes:
you owed tax or received a large refund when you filed your personal
income tax return for the past year
Make a change to the form, send it to your employer, and then see if the changes do what you expect. Then either keep the changes or make more changes.