Four of the firm's six outlets are in the city, with the other two in Hamilton and Matakana.
"We are seeing strong, double-digit growth across our business, on a same-store basis."
He said Nosh's expansion plans would be "very much consumer led".
"If we think there's good interest in a new town then we'll look at that."
But Beuvink said the growth would initially be Auckland-focused, as there was plenty of room for more outlets in New Zealand's biggest city.
"We've got nothing on the [North] Shore, nothing further south or west - we could open a heap more stores in Auckland."
Beuvink said franchising was also a possibility, adding that the success of Foodstuffs' New World supermarkets - many of which were owner-operated - highlighted the benefits of that business model.
At present, all Nosh outlets belong to the company, which is owned by about 12 investors, with founders Beuvink and Chris Moore holding the bulk of the shares.
Nosh opened its first site in Glen Innes in 2006.
New Zealand Retailers Association spokesman Russell Sinclair said there were opportunities for niche operators like Nosh.
"It's a matter of finding a point of difference that distinguishes you from the mainstream players."