The county is seeking the services on behalf of its roughly $131.6 million investment portfolio.
The retirement plan is relaunching an RFP after the recent conclusion of its last search did not yield a hire.
The retirement fund added one new commitment and increased another pair last month.
Co-Investment Fund VI closes with an oversubscribed $2.5 billion in committed capital.
City manager and council approval of a selected firm are scheduled for Aug. 10.
The latest flagship fund closed with approximately $2.4 billion in total capital commitments.
The retirement system added commitments to one new and one existing manager relationship last week.
The new head of business development on the private equity team joined from Monroe Capital.
The pension fund approved the search for one or two managers last week.
The retirement system moved to a new general investment consultant in the first quarter after cutting ties with its incumbent after roughly 15 years.