ACT leader David Seymour says progress has been made on tax, and the parties are looking at ministerial positions as well as policies now.
He spoke to media after a day of meetings negotiating the formation of the government with National and New Zealand First that included the first face-to-face with all three party leaders at a hotel in Auckland.
National subsequently met with both parties separately.
Seymour explained a cut on his face was from the razor that morning. Much like his shave, the parties were getting "closer by the day" to reaching agreement.
He said ministerial positions as well as policies were now being explored in the talks.
"I'd say we're talking about both at this point," he said.
He said progress was being made on tax, which emerged in recent reporting as a likely sticking point in the negotiations.
"We've made some progress on tax, I think us and New Zealand First probably have different tax issues and we'll keep working on those," he said.
"It's mathematical but I think where there is agreement, everyone wants to end government waste and have the average person paying less tax, it's just a question of what the structure of that is."
The Treaty of Waitangi and its principles is another topic of controversy where the different parties have their own stances. ACT campaigned for a referendum on it.
Seymour on Wednesday said they were getting close to reaching agreement on the matter with the other parties, but were not there yet - and did not give away the details of what such an agreement might look like.
"It's obviously an area that we believe is important for the future of New Zealand, we've made a lot of progress there and I think we're pretty close."
The trio were meeting in Auckland after both Seymour and Luxon travelled to Wellington, with expectations of putting together a three-way meeting - but in the end Peters did not travel to the capital.
Seymour said Auckland was the home city for all three leaders - as well as his deputy Brooke van Velden, but whether a final agreement would be reached in the city of sails was "well above my pay grade".
He denied any kind of relationship problems between the three.
"I don't believe that there is a relationship issue on my behalf. I don't hold any grudges or feel that anyone's acted improperly there, obviously I can't speak for the other two but as far as I'm aware they don't have any relational issues because of that as well."