Since the 'Bazball' era began, Ben Stokes' side have won eight of their 10 fourth-innings pursuits, including a new English record of 378 against the same opposition at Edgbaston 18 months ago.
Speaking after that match, Stokes said: "There was a bit of me that wanted them to get to 450, just to see what we'd do".
Now, he is one step closer to finding out after India were bowled out for 255 in 78.3 overs on Sunday, with Shubman Gill's 104 anchoring India's second knock.
"We've got so much quality in our dressing room and there are guys in there who can maybe get 150 for us and win us the game," said England veteran James Anderson.
England ended day three on the attack on 1-67, speaking volumes for the way this team have raised expectations, not least in Hyderabad last week where they overturned a 190-run first-innings deficit to win the first Test.
India's captain Rohit Sharma gets cleaned bowled by James Anderson. (AP PHOTO)
But the challenge of finding another 332 runs in Visakhapatnam is now even steeper, with a tricky turning pitch bringing the home spinners into play and the dynamic Jasprit Bumrah leading the attack.
England lost Ben Duckett for 28 when he was well caught off bat and pad but they refused to back down, Zak Crawley reaching 29 not out and Rehan Ahmed throwing the bat in a late cameo as the so-called 'nighthawk'.
England's inexperienced bowling attack, featuring three young spinners with three Test caps between them coming into the match, performed well again, with Tom Hartley once more leading the way with 4-77.
At 4-211, with Gill on 104, England were facing the prospect of being batted out of the game but England took the next six wickets for 44.
India had started the day 171 in front and with all 10 wickets intact, but old stager Anderson, now 41, blew away the India openers.
He struck with his fourth ball of the morning, a beauty that stood up off the seam and hit the top of Rohit Sharma's off-stump as he looked ruefully over his shoulder.
Yashavi Jaiswal, following up his stunning double century, was next to succumb to Anderson's unforgiving line and length as he flashed a drive to slip.
Racing 20 metres as the ball sailed over his head, Ben Stokes then produced some magic, tracking Shreyas Iyer's big hit perfectly and diving at full length to pull off a remarkable catch to get rid of a danger man on 29.
Gill brought up his third Test hundred in 132 balls, but Shoaib Bashir finally got him when he gloved a sweep behind.
A major concern for England is the fitness of key batter Joe Root. He took a blow to the finger in Sunday's warm-up and another while fielding at slip in the morning session, forcing him off the field for treatment.
"His finger isn't great. Hopefully he'll turn up at the ground and be okay to hold a bat," said Anderson.
