Two New York Democratic State Senators, James Skoufis and Brad Hoylman, have introduced SB 437. It would move the New York presidential primary from April to late June, so that the primary for other office would be combined with the presidential primary.
Ironically, if the bill were enacted, it would conflict with Republican and Democratic national rules, which do not permit presidential primaries later than the first week of June.
In 2020, New York held presidential primaries in late June, and the national parties overlooked the rules transgression. New York had cancelled its presidential primaries in 2020, but then the state courts had ruled the cancellation was unlawful, so they were held late.