Taylor described it to ABC News as a "cleanup crew for the Republican Party," which is also planning reforms for the post-Trump era.
Two current senior administration officials who are debating whether to reveal their identity have already signed on, according to a source familiar with the project.
The group is called the Republican Political Alliance for Integrity and Reform or REPAIR for short and is made up of "former U.S. officials, advisors, and conservatives -- organized by ex-Trump administration officials -- calling for leadership change in the White House and seeking to repair the Republican Party," according to its website.
In a statement Monday, Taylor said that the group is working to get as many as 40 Republican former officials signed on to the effort, according to Politico, which first reported the news.
Last week Taylor likened his time working with the While House with playing "whack-a-mole with bad presidential decisions" on ABC's "Good Morning America." He warned then that his public comments were just the "opening salvo" for former administration officials coming forward to tell unflattering stories witnessed first-hand inside the administration.
"The president can expect that in the coming weeks and months leading up to the election, he is going to hear from more people that served in his administration, and he's going to hear more of them give the same testimonies I gave which is that he's ill-equipped to hold the office that he has and that a second term would be more dangerous than a first term. You'll hear that soon," Taylor said last Tuesday.
He first went public with his criticism of the president and endorsement of Biden last Monday in a video released by Republican Voters Against Trump, a group founded by former Weekly Standard Editor Bill Kristol, which is providing initial funding for the REPAIR group until it can operate as a standalone organization. The REPAIR website currently labels the group as a "a project of Republican Voters Against Trump."
Taylor has already appeared in a series of videos put out by Republican Voters Against Trump to boost Biden's candidacy, and more ads featuring REPAIR members are expected heading into the election.
In a tweet Sunday, Taylor made a call to "people of conscience" still serving in the administration and those who, like him, who have departed.
"There are people of conscience still left in the Administration and others who've departed. They should come forward to say what we all know to be true, what we all witnessed: Trump is unfit for office—and we cannot allow him to debase and divide us," he said in a tweet.
The president, responding to Taylor's endorsement of Biden last week, called him a "disgruntled employee" and claimed he had never heard of him.
Taylor, in response, tweeted a picture of the two together -- with their thumbs up -- in the Oval Office.
REPAIR’s first big project, titled "Publius Reawakened" -- using the collective pseudonym the founders used in the Federalist Papers -- will be a series of anonymous pieces on why the writers believe Trump has damaged the Republican Party and nation -- and how to repair it.
Taylor's coalition is the latest instance of Republicans speaking out against the sitting president, coming on the heels of 27 former GOP congressional lawmakers and more than 70 former national security officials coming out in support for Biden.
The Biden campaign on Tuesday also said it's picked up endorsements from Republican appointees and legal experts from the Reagan administration and both Bush administrations in "light of the corruption and abuse of power that has pervaded the current administration."
ABC News' Molly Nagle contributed to this report.