A San Francisco wine magnate pleaded guilty Tuesday to paying $50,000 for a test proctor to correct his daughter’s SAT scores and agreeing to bribe a University of Southern California athletics department official to secure his daughter’s spot on the water polo team even though she was not a top athlete.

Agustin Huneeus Jr., 53, already stepped down as CEO of Huneeus Vintners, but on Tuesday he pleaded guilty to conspiracy to commit mail fraud and honest services mail fraud as part of the nationwide college admissions cheating scandal.

He issued a written statement Tuesday afternoon outside of the Boston federal courthouse, apologizing to his family, friends, colleagues and other “students who work hard to get into college on their own merit, as well as to their families.”

“With my plea today, I am taking full responsibility for my wrongful actions. My life has been devoted to my family and the people I have worked with and for. I have disappointed them all and brought shame on myself and the people I love,” Huneeus said. “While I wish I could go back and make different and better choices, of course I cannot. What I can do now is to say: I am sorry and I apologize.”

He joined former New York attorney Gordon Caplan in the Boston courthouse in what will be a busy week at the courthouse. Six more parents are scheduled to plead guilty this week, including two more Bay Area parents. A total of 33 mothers and fathers have been implicated in the scheme alleging wealthy parents paid large sums of money to a bogus nonprofit that would use the money to bribe test proctors, university officials and college coaches. Ringleader William “Rick” Singer already pleaded guilty to multiple charges.

The pair appeared before U.S. District Court Judge Indira Talwani, and are the 12th and 13th defendants to plead guilty of the 50 defendants charged. Both men face a maximum of 20 years in prison, but prosecutors have recommended the low end of sentencing guidelines for their guilty pleas. Prosecutors have recommended Huneeus serve 15 months in prison, among other financial penalties, and Caplan between 8 and 14 months.

Both will be sentenced in October.

On Friday, Marjorie Klapper, a 50-year-old jewelry entrepreneur from Menlo Park, is expected to plead guilty to similar charges as Huneeus Jr. Over the weekend, the Wall Street Journal reported that Klapper took the advice of Singer to falsely claim that her son was black and Hispanic on his application. Her son was one of many white children intentionally misrepresented as a minority in an attempt to gain an advantage in the admissions process, the paper reported.

Klapper’s attorney did not respond to a request for comment.

At a previous hearing in March, Assistant U.S. Attorney Eric Rosen listed Singer’s various schemes, including “lying about students’ ethnicities and other biographical information in an attempt to take advantage of perceived benefits from affirmative action and other programs.”

Singer said in court that “everything that Mr. Rosen stated is exactly true.”

Another child had a distant Native American ancestry and identified himself as Native American on his application, according to the newspaper.

As for Huneeus, the wine businessman was prepared to pay $250,000 to Donna Heinel, a senior USC administrator, to accept his daughter to the water polo team with the understanding she would not play on the squad.

“You understand that (my daughter) is not worthy to be on that team,” Huneeus told Singer in recorded phone conversations, according to court records, before asking, “And is there a risk that this thing blows up in my face?”

Singer eventually sent the USC official a fabricated athletic profile of Huneeus’ daughter, including a photograph of another girl playing water polo.

Caplan paid Singer $75,000 for his accomplice to correct his daughter’s ACT test answers.

On Wednesday, Peter Jan “P.J.” Sartorio, a 63-year-old Menlo Park packaged-food entrepreneur, is scheduled to plead guilty. Sartorio is accused of paying $15,000 to have a proctor cheat on his daughter’s entrance exam.

Matthias Gafni is a San Francisco Chronicle staff writer. Email: matthias.gafni@sfchronicle.com Twitter: @mgafni