Almost half of Te Papa's management roles are proposed to be axed under a "significant" restructure.
The national museum last week announced plans for a two stage process in an effort to cut costs.
Now, Te Papa staff were being asked for their feedback on the first of two proposals.
Final decisions on both proposed phases would be implemented in April next year.
In announcing the restructure last week, the museum said the review would ensure its financial sustainability now and in the future.
An internal document seen by RNZ shows management roles could be halved - from 41 to 22.
Some new roles would be created.
The organisation's co-leaders, chief executive Courtney Johnston and kaihautū Arapata Hakiwai, would keep their jobs - among 10 roles to be reconfirmed.
Staff in the remaining roles proposed to be disestablished, would have to submit expressions of interest for a range of new positions.
The proposal would see those directly reporting to the co-leaders - currently, five directors, a chief operating officer, and the head of governance and strategy - reduce from seven roles to four.
The chief operating officer's role is among those to be reconfirmed, and is proposed to be joined in the second tier of management by a deputy chief executive of collections and communities, a pou whakahaere kaupapa Māori, and a deputy chief executive of experience and audience development.
Seven roles were to be retained in the third management tier under the proposal including, the head of the biodiversity research centre, chief people officer, pou reo, and pou tikanga.
Overall, the proposal would see the 33 roles reduce to 16 in the third tier.
In a statement to RNZ, Johnston and Hakiwai said the proposed changes at the management level were significant, but would "create efficiencies and enable us to work together in new ways".
They said the proposed changes for the next phase had not yet been determined.
"Our work with iwi and Mana Whenua, and delivering on our commitment to Te Tiriti, are vitally important and will remain at the heart of the museum's work.
"Out of respect for the needs and mana of our people, we won't be commenting any further while this internal process is underway."
Last year, Te Papa started charging international visitors to the site due to rising costs of energy, insurance and staffing.
Johnston and Hakiwai last week said rising costs and maintenance of specialist buildings have put a strain on cash reserves.
"As kaitiaki of the national museum, we've made significant operational savings and increases to our revenue, but we need to do more."
The restructure review would be carried out in two stages, with the first phase completed this year and focused on "tier two and three" managers.
Phase two would occur early next year and would centre on the rest of the Te Papa team.
The museum co-leaders said existing work programmes - such as the repatriation of kōiwi tangata and kōimi tangata, their strategic, founding, and long-term partnerships, and work with iwi and Mana Whenua - would also remain unchanged.
"Our commitment is to make this process as transparent as we can and respect the needs and mana of our people."
The document stated Te Papa received $43 million in Crown funding annually and had to raise at least $38m a year through commercial activities, philanthropy, and partnerships.
But rising operational costs - including maintenance of ageing and "highly specialised buildings" - was contributing to an expected cash shortfall of $4.3m this year.
As of September, that shortfall was projected to rise annually.
