"second more significant" is a grammatically correct phrase and can be used in written English.
It is typically used to compare the significance or importance of two things, with the second one being the more significant. Example: In terms of economic impact, the first wave of the pandemic was significant, but the second, more significant wave had a much greater effect on the global economy.
A second, more significant downturn has occurred over the past decade.
So Kerry is asking for a three-month grace period on the second, more significant resolution, in which all sides sweat out the Israeli election results with him.
A second, more significant, new anthology, "The Moral Obligation to Be Intelligent," edited by Leon Wieseltier, shows just how much is at stake.
The second – more significant – point is that even with the use of the PPP method, real living standards in China remain well behind those in the US.
The proposed indices (ii) and (i) presented the most and second more significant p-Values (p < 0.001 and p = 0.001), respectively.
The second, more significant challenge relates to the loss of board awareness of the contributing factors to Sarbanes-Oxley: the governance failures of the Enron board.
Then, too, his dip in the polls could be Trump-related, as in, "Wait a second, you mean that's what it would be like here?" The second and more significant point is that, even if he were to win more votes than the other candidates, it's unlikely that Wilders would become Prime Minister.
The first alternative may somehow limit Chinese potential for expansion and the second brings more significant risks and responsibilities as well.
The second is more significant: no one steals money if they can't keep it.
Second and more significant, the Lincoln Center faithful, entirely unfamiliar with the Ta'ziyeh tradition, do not provide what a hometown crowd would.
But there was a second, slower, more significant opening, which required actual understanding -- of Buddhism, for example, and the traditional arts of judo and the tea ceremony.
