Clemson players Seth Beer, Ryley Gilliam, Ryan Miller and Chris Williams were selected, as were Tigers recruits Parker Meadows and Charles Mack.
South Carolina players Carlos Cortes, Adam Hill, Cody Morris and Madison Stokes were drafted. So were USC recruits Owen White and Taj Bradley.
Coastal Carolina's Seth Lancaster and Kevin Woodall Jr. were drafted, as was Wofford's Adam Scott.
Rounds 11-40 are set for Wednesday.
44. Tigers: Parker Meadows, Grayson, Ga., Clemson recruit
83. Mets: Carlos Cortes, listed as 2B by Mets, South Carolina
189. Diamondbacks: Ryan Miller, RHP, Clemson
223. Indians: Cody Morris, RHP, South Carolina
287. Phillies: Madison Stokes, SS, South Carolina