The phrase "again asserting" is correct and usable in written English.
It can be used when you want to emphasize that someone is repeating a statement or claim they have made previously.
Example: "In his latest speech, the politician is again asserting his commitment to environmental policies."
Alternatives: "reiterating" or "reaffirming".
Rodriguez and Voeckler again did battle for the mountain points, with Rodriguez again asserting his dominance.
He picked up again, asserting that Mr. Obama's ascendancy to the White House "makes us think that we could accomplish anything when you put your mind to it".
With the rerelease of "Titanic," the society wants Mr. Cameron to pay again, asserting that the 3-D version is a new work, not covered under the previous agreement.
Campaigning in Pennsylvania, Mr. Bush reacted to a Senate Intelligence Committee's report criticizing the intelligence agencies by once again asserting that Saddam Hussein had posed a threat to the United States and other nations.
After dropping out of pharmacy school for declining to dissect a frog, Rauschenberg was drafted into the navy in 1944, where he was made a neuropsychiatric technician in the Hospital Corps after once again asserting his refusal to kill.
Emerson reclaimed an idealistic philosophy from this dead end of 18th-century rationalism by once again asserting the human ability to transcend the materialistic world of sense experience and facts and become conscious of the all-pervading spirit of the universe and the potentialities of human freedom.
And limits again assert themselves.
Soon enough, reality again asserted itself: the schedule slipped, and costs rose.
And she again asserted that she had been pressured by the State Police.
In such a suit, the Democrats would again assert that Ms. Harris had abused her discretion.
Mr. Drake again asserted that he was a victim of mistaken identity.
