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Some 160 jobs will be be lost in the review, which has been ongoing since the end of 2015.
In April, the university said 86 employees had taken voluntary redundancy, and the university said on Wednesday the total was now 106.
University HR director Kevin Seales said the university was on track to informing the majority of staff whether positions had been changed or not by June.
Tertiary Education Union organiser Shaun Scott said morale was "understandably pretty low" among support services staff, and a number had been told to expect a letter by the end of May.
Mr Scott said the process had been "far from smooth" and some people were relieved to know they would soon be getting some clarity on their situation.
"Unfortunately it happens when it happens," he said.
An anonymous complaint about the process has been given to the Otago Daily Times, saying that letters had been delivered to the wrong people and staff had been informed while on annual leave that their jobs would be lost.
Mr Seales denied incorrect letters had been sent, and said concerns about people being informed while on holiday had not been brought to the university's attention.
The letter also claimed academic staff were concerned about the changes.
"[They are] wondering how they are going to keep their department functioning as general staff take redundancy, retire early, with little indication of replacements, or even if they are to be replaced."
Mr Scott said the concerns were not new and throughout the process academic staff had been concerned about potential lack of organisation when it came to the running of their departments.
"Until it's implemented we are not going to know for certain.
"From our point of view it is really crucial that where problems are identified that they are listened to and responded to appropriately," he said.
Mr Seales said the university was very confident in the changes it was making.
"The academic departments will function well under the new structure for support services."