Two articles that were published after William J. Hoffman's "Brouwer Beginnings" (published in 1947/48, The American Genealogist [TAG] vols. 23-24) should be mentioned.
"Adolphus Brower (1777-1855)," by Katherine Hewitt Cummin was published in TAG vol. 44, pp. 150-153. This article identifies Adolphus Brower, born 3 July 1777, died 23 August 1855, buried at Greenwood Cemetery in Brooklyn, as a son of Isaac Brouwer and Jacomyntje Quackenbosch. Adolphus was married to Elizabeth Baker on 24 March 1799 in Brooklyn at the house of John Brower (recorded at St. Ann's Episcopal Church). The couple lived in Brooklyn and had nine children, eight of whom were baptized at St. Ann's. William J. Hoffman, in "Brouwer Beginnings," had suggested that this Adolphus Brower was a son of Adolf Brouwer (1725-ca.1780) and Elisabeth Lassing (this couple did have a son named Adolf/Adolphus, but he went to New Brunswick, Canada after the Revolutionary War). Katherine Hewitt Cummin's article corrects Hoffman's suggestion.
"Another Child of Peter (Adam) Brouwer," by Phyllis Miller, was published in the New York Genealogical and Biographical Record, vol. 120 (1989) pp. 44-45. This article adds daughter Maria to the family of Pieter Brouwer and Petronella Kleyn. No record of baptism survives for Maria. She married Jacob Knoet/Clute by banns dated 16 November 1727 at Albany, New York. Hoffman had omitted Maria from the family of Pieter Brouwer. Her placement in the family is based upon Maria naming her eldest daughter Nelletie (diminutive of Petronella) for her mother, and second son Pieter, for her father, and of cross-sponsorships at baptisms between Maria and her siblings Jacob Brouwer (husband of Maria Bovy) and Cornelia Brouwer (wife of Claes Bovy).
I do have a copy of the Pieter Brouwer article available online. It was included in the William B. Bogardus Collection. I do not have a copy of the Adolphus Brower article available. It can be accessed online by those who are members of the New England Historic Genealogical Society at their website American Ancestors.