The Securities and Exchange Commission (SEC) has previously charged two other men - Henry Morris and David Loglisci - with orchestrating the scheme, which rewarded companies that paid kickbacks with lucrative asset management contracts for the New York State Common Retirement Fund.
The watchdog's new complaint alleges that former hedge fund manager Barrett Wissman was a key player in the scheme, arranging some of the payments made to Mr Morris and receiving around $12 million in bogus fees himself.
Meanwhile, ex-New York Liberal Party leader Raymond Harding is accused of receiving approximately $800,000 in fraudulent fees arranged by Mr Morris and Mr Loglisci.
Mr Wissman has agreed to a partial settlement of the SEC's charges without admitting or denying the allegations. Financial penalties and disgorgement will be determined at a later date. The charges against Mr Harding remain pending.
According to Bloomberg, Mr Wissman has also pleaded guilty to criminal charges brought by New York attorney general Andrew Cuomo in relation to the case.