Propelled by a hundred from Jonny Bairstow and match figures of 10 for 45 from James Anderson, England thrashed Sri Lanka by an innings and 88 runs in the first Test at Headingley last week to go 1-0 up in the three-match series.
But Broad, still the world's number one ranked Test bowler, said there was no danger of England letting up when the second Test starts at north-east county Durham's Riverside headquarters today.
"With a Test series up for grabs we're on it and our aim is to have all nine Test trophies and we can make it eight this week," he added yesterday.
"I think Australia and South Africa have done it before. It is not something that has been done a huge amount, so it would be a huge achievement and we're desperate to do that.
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England will have to make at least one change after Durham all-rounder Ben Stokes was ruled out of playing on his home ground with a knee injury suffered at Headingley.
Warwickshire's Chris Woakes, a like for like replacement, was called into the England squad on Monday and promptly took a career-best nine for 36 against Durham at Edgbaston.