The Seawolves offer was the first for the 6-foot-5 Naperville, Ill., native, who also plays AAU basketball for the Young & Reckless organization.
James has already eclipsed the 1000-point mark at Bridgeport Prep.
The 6-foot-4 Bumbray also holds an offer from Virginia Union.
Harrison also plays for the Corey Graham Elite 17U UA Rise Circuit.
In addition to the Binghamton offer, the 6-foot5, 185-pound Sims holds offers from New Mexico State and Alabama A&M.
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The 6-foot-2-inch, 175-pound point guard scored 2,658 career points and earned Ohio's male Gatorade Basketball Player of the Year and the Co-Ohio Division II Player of the Year honors.
The 6-foot-10 London, England, native averaged 4.0 points, 2.0 rebounds and 1.4 blocks per game while connecting on 58 percent of his shots from the field this season.
The 6-foot-11 big man picks up his first D1 offer.
The 6-foot Stewart averaged 11.4 points, 2.7 rebounds, 2.2 assists and 1.1 steals per game in 26 contests played this past season for Neumann-Goretti Catholic High School.