Maguire, 28, made four birdies in her final six holes to lead a major at halfway for the first time.

"This is uncharted territory for me," said Maguire.

"Whatever happens this week, I'm sure I'll learn a lot, and just sort of taking it one day at a time.

"I think this golf course demands that. I think you can't think more than one shot ahead, let alone a hole or a round ahead."

Maguire, who was three shots off the lead after day one, is one of the form players on the circuit after she stormed to her second LPGA Tour title on Sunday at the LPGA Classic.

At New Jersey's famed Baltusrol, Reid's round of 67 moved her up to four under par, tied for second alongside China's Lin Xiyu and Norway's Celine Borge.

First-round leader Lee-Anne Pace of South Africa and Australia's Minjee Lee - who is chasing her third major title - are a shot further behind.

For Reid, her promising run at the second major of the year comes just nine months after she exited the sport due to a wrist injury.

"I legit quit," she said. "When I got my injury, I tried to play through it, which I kind of felt I had to. In September I literally told Carly [her wife], I'm going into the media, I'm not playing golf anymore.

"With things like that, if you just give me a bit of space, I do kind of work it out myself.

"I missed the competitiveness of it and I thought let's give it one more go. I've just been really enjoying myself this year."

Northern Ireland's Stephanie Meadow is the only other British player under par after two rounds, as one of eight players - including top-ranked Ko Jin-young - on one under.

But England's Georgia Hall, Charley Hull, Bronte Law and Laura Davies all missed the cut, as did world number two Nelly Korda, fellow American and world number four Lilia Vu and Thai number six Atthaya Thitikul.