The phrase "assert that much" is correct and usable in written English.
It can be used when you want to emphasize a strong belief or claim about a particular point or issue.
Example: "While I understand your perspective, I cannot assert that much without further evidence to support the claim."
Alternatives: "claim that much" or "maintain that much".
Union officials acknowledge that the city will save money by no longer having to pay their salaries, but these officials assert that much of these savings will be erased because the city may soon start paying their welfare checks.
Bivens and Mishel define "rent" as income "in excess of what was needed to induce the person to supply labor and capital," and they assert that much of the income of the top 1 percent has little to do with productive economic activity and could be taxed away without harm to the economy.
They assert that much debate and discussion in politics would not be intelligible were it not for the fact that citizens are willing to engage in open minded discussion with those who have distinct morally informed points of view.
Haggith and Newman assert that much of the rest of Harlan's film is "pure invention".
Critics assert that much original work by Michelangelo – in particular pentimenti, highlights and shadows, and other detailing painted a secco – was lost in the removal of various accretions.
The mutational-hazard (or mutational-burden) hypothesis [ 1] asserts that much of this observed variation in genome compactness can be explained by the product of the effective genetic population size (represented in this study as the effective number of gene copies at a locus [ N g ], not individuals) and the mutation rate.
(p. 1) And addressing physicians, Guttmacher and Collins (2002) as editors of the New England Journal of Medicine, assert that … Much is known, but much remains mysterious.
Enforcers such as Darren McCarty advocated letting the opposing enforcer get a few punches in before putting in maximum effort, and assert that fighting is as much about knowing how to take a punch as it is about delivering punches.
(Given Mr. Hester's recent lawsuit against A&E asserting that much of the original "Storage Wars" is staged, there may be some truth to this).
The SJP-Demetrakis team asserted that much of its financing would come through SJP's relationship with Prudential Real Estate, a partner of SJP on numerous projects over the last 20 years.
For example, as long ago as 1995 he was asserting that much of the New Deal, and thus much of the contemporary work of the federal government, was unconstitutional.
