Memphis United Representatives and the Mid-South Peace and Justice Center want City Council Members to approve several changes to the group.
They presented a proposed ordinance to council on Tuesday.
A group of law students from the University of Memphis presented a proposed ordinance to them Monday.
They said the board needs subpoena powers, staffing and a website where people can easily submit officer complaints.
Although the groups agreed on some issues, some still have concerns about subpoena powers.
This topic will be brought up again in Tuesday night's council meeting for its first reading.