The West Indies believe they have the batsmen to defy New Zealand, despite the mammoth task facing them to save the second Test in Hamilton.
The tourists will resume on the fourth day at 2-30, ambitiously eyeing what would be a world record chase of 444, or more likely trying to survive for two days.
Captain Kraigg Brathwaite is 13 not out and Shai Hope is on one.
West Indies batting coach Toby Radford was disappointed they lost two wickets late on day three after previous good starts in the series, although they are 1-0 down in the two-match series.
He did not believe he had to tell the players to temper themselves.
"You've seen Kraigg bat, he can bat all day, bat six or seven hours. Shai Hope also plays that way," he said.
"The middle order. Roston Chase has had a very good year, scored hundreds against Pakistan. It's about doing it here isn't it?
"Here it's a bit more swing, (Tim) Southee and (Trent) Boult bowled very well. It's been a different Test I think and it's coping with that and coming up with methods to play that."