Sydney Beveridge has a piece on Gotham Gazette about the elections in New York and notes that there is room for a few more.
Of 65 seats in the State Assembly representing New York City, only 20 primaries are planned (all but two of which are for the Democratic Party). These numbers keep declining as candidates are removed from the ballot at the last minute. This scant number of primaries is typical throughout the whole state. Less than one in five New York City voters registered with a major party will have a reason to go to the polls September 12th and even fewer will be confident that their vote could make any difference.
She goes on to write:
In 2004, New York City could have had as many as 130 Assembly primaries, but had 17, and 60 Senate primaries, but had 12.
— Azi Paybarah