But because of legal obstacles and complications in getting co-operation from NGOs and private organisations, very few "Approved Information Sharing Agreements" have been signed off.
Mrs Tolley said if such an agreement had been in place, Emma-Lita's dangerous circumstances might have been picked up.
"If she had a brother or sister that was ill, it might have flagged that there was something happening. And that's the frustration of what we're trying to achieve."
The minister took a shot at some NGOs, saying they had "flat out refused to be part of any information-sharing agreement".
"It's fraught with difficulty," she said. "Many professionals are trying to protect themselves. It's very frustrating because at the heart of it, we're trying to keep children safe.
Asked for an example, she said: "A child is being neglected, and the mother has mental health problems. A health professional is dealing with the mother. But without an approved agreement, that health professional is reluctant to hand over information about the mother but that is protected under privacy laws."
One of the only existing agreements, in Hamilton, requires police, health, education, social development, and Child, Youth and Family officials to securely share any information which may be relevant to other agencies.
Mrs Tolley said Housing New Zealand could also be a part of future agreements and the Ministry of Social Development, which assessed housing tenants' needs, was also likely to be included in any cross-agency collaborations.