Any expansion might also open the door to pay TV, something the Freeview electronic programming guide is already technically capable of providing.
I would expect TVNZ to take the platform towards accommodating online pay TV, competing with Sky
But expanding Freeview would mean additional investment and that raises questions about whether the shareholding might change.
While Freeview has received taxpayer funding, it is a private company owned by four broadcasters: MediaWorks, TVNZ, Maori TV and RNZ.
Adams said: "The TVNZ board is the major shareholder of Freeview, and I would expect them to be actively thinking about how best to increase the value of its investment and to that end what future investment requirements might be.
"TVNZ have indicated to me that it's something they're interested in looking at," she said. "I've invited them to send me a formal proposal and will consider it in due course."
Ready to invest?
In my opinion, the question is whether the current shareholders can or will make the necessary investment.
I would expect TVNZ to increase its current 44 per cent stake to further dominate Freeview. MediaWorks is the next biggest shareholder.
There have been rumours of closer ties between TVNZ and Mediaworks. An expanded Mediaworks investment in Freeview might make sense, though MediaWorks would surely resist if TVNZ held a dominant stake. MediaWorks declined to comment.
For Maori TV, spokesman Rick Osborne said: "Maori Television remains committed to working with other Freeview shareholders to advance the continuing development of the platform."
Officially, RNZ is relaxed. Its head of business transformation strategy, Alan Withrington, is currently chairman of Freeview. RNZ said in a statement: "A lot has changed in the media environment in the last decade and like any responsible business organisation regular strategic reviews are important for future planning."
Given that RNZ has been starved of government funding for years, it is not clear that RNZ could afford extra capital investment if Freeview was expanded.
TVNZ & Spark
Television New Zealand wants Freeview to become a Kiwi bulwark against Google and Facebook. That makes sense to me. But in my opinion there are risks in Freeview becoming seconded to a new role supporting TVNZ's commercial aims, such as pay TV.
TVNZ's Kenrick plays down the notion that there are plans to move beyond 44 per cent. He says he would prefer Freeview to continue with multiple shareholders, to spread the load of any extra investment.
TVNZ has been in talks with telecommunications company Spark about a joint venture linking its online distribution network with TVNZ's media expertise,
In my opinion, dominance of Freeview would make a TVNZ joint venture more attractive to Spark, which badly needs programming support for its Lightbox pay TV venture.
Both companies need to link telecommunications with content, now that Vodafone plans to merge with Sky TV.
Better on the box
Television New Zealand and MediaWorks are in talks to revive a joint industry body to promote TV as a medium to advertisers and marketers. The networks abandoned a similar body called Think TV during the Mark Weldon era.
TVNZ commercial director Paul Maher said both he and new MediaWorks CEO Michael Anderson saw the need for an industry-wide approach.
Maher stressed TVNZ was heavily invested in digital. But advertisers and marketers were moving too fast and needed to be reminded that TV viewing was more valuable than online hits.
"Marketers have moved 1 per cent of the market away from TV each year despite its cost staying low," Maher said.
Facebook has been reported as overstating audiences for video ads.
But, says Maher, "I've been surprised there has been little reaction from the advertising and marketing sector.
"If I went to the market and said our prices have been overstated by 70 per cent I would be crucified.
"Big media owners have significant reach and advertisers are now saying that reach is important".
Other players such as Herald publisher NZME have made inroads into taxpayer funding for short-form video, but Maher does not see that as a major threat.
"The model for short-form video is still evolving. Long-form is more accessible on platforms."
John Drinnan produces the media website zagzigger.com