The University of Otago's council would include two staff representatives and the student association president under a proposal released for consultation last week.
Tertiary Education Union organiser Shaun Scott said the union was initially pleased with the draft constitution, which recognised the need to retain staff and students on the council.
''But we still do think that staff and students should make up a third of the council, so our submissions will be pushing for a fourth [student and staff representative].''
Mr Scott said the union was developing its response and talking to members.
The draft constitution came after an amendment to the 1989 Education Act put a 12-member cap on tertiary education institutions' councils and removed a requirement for there to be at least three student- and staff-elected council members.
Previously, Mr Scott had described justifications for the amendment as ''spurious'', and said ''We'd like to see a third of the council held aside for elected student and staff representatives''.
The draft constitution proposes a 12-member council, six members fewer than its current size.
Under the proposal, students would lose one seat, and staff members two.
There would still be four ministerial appointees under the amendment.
In response to the draft, OUSA president Paul Hunt said only: ''OUSA believes there should be two student representatives on the new University Council''.
The consultation will be open until June 20, and the new council will need to be in place by July 1, 2016.