"further reassured" is correct and usable in written English.
You can use it when you want to emphasize that someone was already reassured, but is now even more so. For example: "The child was reassured by their parent's presence, and further reassured when the teacher arrived."
A convincing victory for Emmanuel Macron, in France, has further reassured those who were preparing to mourn "the end of Europe".
Carlyle, who with his wife consoled the distraught Mill that night, later further reassured him in a generous, almost gay, missive.
We are further reassured that the Earth has been bombarded for billions of years by cosmic rays far more powerful than anything the collider will produce without, so far, being sucked into a black hole or turning into uninhabitable yuck.
He certainly did not, and as he walked into the dugout he doffed his cap to the fans, who would be further reassured two innings later when Jim Johnson, the closer who imploded the night before in Baltimore's 7-2 loset set down the Yankees in order in the ninth, striking out Alex Rodriguez to seal the win.
I, for one, was further reassured over lunch in Urla, about 20 miles from Izmir, at another state-of-the-art winery run by Can Ortabas, who took up growing grapes after he discovered ancient sets of vineyards on his land.
The stock market returned to record levels on Thursday after Morgan Stanley and other companies reported better-than-expected earnings and investors were further reassured by the Federal Reserve's chairman, Ben S. Bernanke, who emphasized once more that the Fed was committed to stimulating the economy.
Marshall's custom of speaking in long strings of football metaphors further reassures the legislators.
The film further reassures by ridding him of any troublesome sexuality.
Before the gulf region's markets open on Monday, the U.A.E.'s central bank might consider further reassuring depositors about where it stands as a lender of last resort.
But the trial results, though limited, could further reassure the many pregnant women who have already been vaccinated or who have been nervous about getting the shots.
Hulstrand further reassures reluctant downsizers that, "Asking yourself why it's so hard to do and allowing yourself time to acknowledge and deal with the emotions can help resolve those unsettling feelings".
