There are a few buildings for sale in the neighborhood — thanks to G. for staying on top of the listings. This latest one is 53 Beach, on the northwest corner with Collister. I think of it as the WeWork building, but it was also home to Montessori School of Manhattan, which closed in 2017 when it lost its lease. The building is part of the Tribeca West Historic District, and I have added some info from the designation report below.

53 Beach has changed hands only a couple times in the past 60 years. The first record on file goes back to 1966, when Westinghouse Electric sold the property to Appliance Packaging & Warehousing for what I think was $142,000. By 1970, Appliance Packaging & Warehousing was bankrupt, and the property was transferred to an entity called Beach & Collister. After a few more transfers, it appears to be sold to Steven Ehrlich and Harold and Herbert Wegweiser in 1985 for $1.25 million. Over the next 40 years or so, the owner mortgage the building several times but never sell until now. The listing is for $40 million.

It was built in 1915 as a industrial warehouse and was converted (my guess, from the mortgages) to offices in the mid-nineties. The listing says it will be delivered vacant.

From the Tribeca West Historic District designation report, 1991
The building replaced two early-nineteenth-century buildings on the site. Designed by architect Oscar S. Teale, the building was commissioned in 1885 by Joseph Naylor, founder of a building contracting and real estate firm; Naylor also erected on this block the store and loft building at 405 Greenwich Street (1886), as well as others in the district.

The functional design of the brick warehouse-type building, originally used as a factory, reflects the interior framing with the piers, expressed as buttresses rather than decorative pilasters, dividing the facades into bays with two segmentally-arched windows. Round arches in each of the street facade bays feature a granite keystone; the loading bays appear to have been originally the western two bays of the Beach Street facade where iron bands protect the brick piers and a loading platform has been built over the stepped vault.

A late 1980s renovation of the building included the removal of fireproof shutters on the Collister Street facade and the insertion of glass-block infill in the arched openings of the base. From the mid-1920s through the 1940s the Loring Lane Company used the building for wood and willow ware sales and storage. From the 1960s to the 1980s the building was occupied by the Appliance Packing and Warehousing Corporation.