McCarthy set a 36-hole course record at TPC River Highlands with a 15-under-par 125 total, with Bradley matching it several hours later to share the halfway lead.
Following Thursday's red-hot round of 60, McCarthy carded a five-under 65 after recovering from a bogey on the par-4 second hole, his first and only blemish of the tournament so far.
"It's nice, but golf tournaments aren't 36 holes unfortunately, so I know there is still a lot of golf left," McCarthy said.
"I'm playing some really nice golf, so I'm looking forward to having fun this weekend and I'm looking forward to the challenge."
After McCarthy's magical mark, it was Bradley's turn. Following an opening-round 62, he used a run of five straight birdies on the back nine on Friday to card a seven-under 63.
The pair hold a three-shot lead over fellow American and 2019 champion Chez Reavie, who posted a second-round 63.
Eric Cole (65) is outright fourth at 11 under, one shot in front of Zac Blair (65) and Scott, who continues to lead the Australian challenge at 10 under despite only managing a 68.
Scott had opened his challenge on Thursday with a sizzling round of 62 featuring 11 birdies.
"A bit of a slow day compared to yesterday. Still was 68," he said.
"Wasn't quite firing on all cylinders. Missed a few fairways, missed a few greens, and missed a few putts that looked pretty good.
"Just didn't really get the momentum going but hopefully that's my slow day for the week."
Lucas Herbert soared into contention with a 64 to surge to nine under and into a share of seventh with fellow Australian Min Woo Lee (65).
"I'd have taken nine under through two rounds if you offered me that at the start of the week," Herbert said.
"I'm going through a bit of a rough patch with the game so feel like I got those results out there and I'm pretty happy with that.
"I found a little something with my putter yesterday morning before the round. That's really helped. I've putted great the last two days."
After looking like missing a fourth consecutive cut, Jason Day climbed into a share of 41st at five under with a second-round 64 ignited by five front-nine birdies.
Cam Davis is also five under following an even-par 70.
- with AAP
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