The pension plan liquidated its approximately $1.9 billion global equity mandate and made commitments totaling $1.6 billion in March.
The plan is looking for general and private markets consulting services.
The city expects to generate a shortlist of candidates to conduct interviews with on July 29.
The pension is seeking an additional core fixed-income manager to handle up to $775 million.
The commitments include a new manager relationship for the plan.
The plan currently works with general investment consultant CAPTRUST Financial Advisors.
The plan is seeking firms to manage a total of $100 million.
The city expects to select a firm by July.
The retirement system opted to pursue entering a contract with a new private debt fund after failing to come to an agreement with a previous selection.
The city received three proposals in response to an RFP issued on behalf of the plan in February.