But Cook would not be drawn on how tall those blocks would be because he said they were still in the planning phase.
Throughout New Zealand, older, more traditional-style retirement villages have been developed as low-rise, often single-level sprawling projects, spread across many hectares of land.
But developers are now trying to maximise their sites, particularly in the hot Auckland market, squeezing more buildings in by developing up instead of out.
Summerset's plans are a clear indication of that trend.
We've got really good demand right across the country. Last year and this year, about 30 per cent of unit sales were in Auckland but that actually leaves 70 per cent across the rest of the country.
At Beachhaven, Ryman Healthcare is building multi-level blocks on the former Fernz conference centre site. At Takapuna, Metlifecare has built a series of blocks at The Poynton near North Shore Hospital.
The financial model behind New Zealand retirement villages is so lucrative or attractive that one of the world's largest businesses, Blackstone, has New Zealand bought villages from Australia's Lend Lease and plans to buy more here.
Kishore Moorjani, a Blackstone senior managing director and head of tactical opportunities, was in New Zealand this month to meet people at the villages it is buying, mainly in Auckland and he was full of praise for the financial system which ensures retirement businesses here are so profitable.
We're always looking and always in the market and when things come up which make sense, then we'll do so.
However, others have questioned whether business should be making so much money from our increasingly aging population and some in the retirement sector have called for new models of ownership, including residents getting capital gain when their units rise in value.
Currently, most owner/operators enjoys that windfall at the expense of the elderly resident.
In the December 2015 year, Summerset built 303 units but it has announced that it plans to lift this by a quarter again to a "build rate" to 400 units this year to meet strong demand and Cook said about 130 new units will be in Auckland.
"About a third of those will be in Auckland: Hobsonville, Ellerslie, Karaka and Warkworth," Cook told the Herald.
But Cook said there were opportunities elsewhere.
"We've got really good demand right across the country. Last year and this year, about 30 per cent of unit sales were in Auckland but that actually leaves 70 per cent across the rest of the country," he said.
Summerset has a land bank which would enable it to build 2414 new units.
"A bit under half is in Auckland and on sites which have already been purchased," Cook said.
"We're always looking and always in the market and when things come up which make sense, then we'll do so," he said.
Summerset is not on the North Shore yet.
The minimum land parcel now is 2.5ha "but we would buy smaller sites in the right locations", he said.
