But far from pushing through a radically new vision as many democracy advocates hoped, they are likely to preserve the Islamic law provisions and grant even greater powers to the military.
Egypt's stormy politics are the reason.
There is only one Islamist politician on the 50-member panel amending the constitution—but his objections have been enough to prevent the secular politicians who dominate the assembly from acting.
At the same time, the military that toppled Morsi is pressuring the assembly to make it virtually independent of—or even above—the elected government. The panel has been sharply divided over an article that would allow the generals, not the president, to choose the defense minister—a sign of the army's wariness of being under the control of an elected civilian.
Democracy advocates warn the provisions could erase other significant democracy gains that are in the final draft still being shaped.
New articles definitively guarantee freedom of faith, expression, thought and the press, better due process and bans on torture, said Bahey Eldin Hassan, head of the Cairo Institute For Human Rights. On the basis of those articles alone, "this will be the best constitution of all Egypt's charters," Hassan said.
But, he said, the controversial articles would "constrain those gains.
Proposed amendments to ban religion-based political parties and lift restrictions on building churches could also run into contradictions with Shariah rules.
And granting an untouchable status to the military could give it political power over the government.
It "will only sow the seed for a military state," said Hussein Abdel-Razek, a leftist politician in the assembly. "This logic is terrifying because it could simply end up with the army in power."
Over the past week, panel members began approving a final draft, voting article by article. But they have only taken up uncontroversial portions, leaving contentious articles for last.
Fearing that Morsi supporters will exploit any sign of division, the panel has been working in secrecy. Sessions, which began in September, are being held behind closed doors—a stark contrast to the Islamist-dominated panel that wrote the constitution during Morsi's year in power, in which sessions were televised.
The draft is to be put to a public referendum in January. Interim authorities are hoping it wins with more than the 63 percent of the vote that the Morsi-era constitution garnered in a 2012 referendum. If the al-Nour Party turns against it, however, that could deeply damage its prospects. Al-Nour is the only Islamist faction that has supported Morsi's removal and the military-backed transition plan.
The constitution has been at the center of hopes for enshrining a new, more democratic Egypt since the 2011 uprising that toppled autocrat Hosni Mubarak.
After his ouster, Islamists surged to power by winning multiple elections, dominating parliament and capturing the presidency in 2012. Parliament formed an Islamist-majority panel to write a new constitution—and it was quickly mired in controversy. Over time, all the non-Islamist members quit, accusing Islamists of ramming through their agenda.
With the courts about to dissolve the assembly, Morsi issued decrees last November granting himself and the assembly sweeping immunity from judicial review. That allowed Islamists to finish writing the document and get it to a public referendum.
But the decrees prompted the first large protests against Morsi, and fueled the growing public perception that Islamists were trying to impose their vision on the country. The anti-Islamist backlash culminated in massive protests by millions that triggered the coup.
Now out in the cold, the Brotherhood and its allies have been crippled by a heavy security crackdown. Egypt's liberal and secular elite are in the rare position of being in the drivers' seat.
Secular members of the assembly have bristled with frustration over compromises forced by the sole Islamist politician.
"This is the golden opportunity" for dramatic changes, said Abdel-Razek, the leftist assembly member. But delegates fear Islamists will campaign against the charter as "anti-Islam" and want al-Nour's support to bolster its credentials.
"The campaign by the Muslim Brotherhood already started," Abdel-Razek told The Associated Press. "And the worry is al-Nour will join them if it fails to impose its vision."
Two key articles are at issue.
Article 2, first introduced in 1971 by then-President Anwar Sadat, states that Islam is the religion of the state and "the principles of Shariah are the main basis for legislation." That article has effectively become untouchable, seen by many as a reflection of the country's Muslim identity.
Abdel-Razek said he tried to propose changes, but the assembly wouldn't consider them. "It was like I was talking to myself," he said.
The vagueness of the word "principles" in Article 2 long allowed authorities to avoid implementing a strict version of Islamic law sought by Islamists. So Morsi's allies introduced Article 219, which gives a firmer definition and would allow Islamists to insist on specific Shariah tenets restricting behavior seen as un-Islamic.
A majority of assembly members now want to remove the article—but they are tangled in efforts to appease al-Nour.
Salah Abdel-Maboud, an al-Nour alternate delegate, said the party is willing to remove it only if some of its language is put in place elsewhere. "We are extremely flexible," he said, but added a warning: "If Shariah-linked articles are touched, all options are on the table."
The debate over the military articles is more complicated.
The proposal giving the military the right to name its own leader has support among a significant sector of the assembly. The article would give the Supreme Council of the Armed Forces the power to name the defense minister, who serves as the military's chief. While the president could remove him, the armed forces council would appoint the replacement.
Assembly member Amr al-Shobaki said the military fears political factions would plot to take over the armed forces by installing generals with their ideology. He said the military's delegate on the panel told him, "What would you do if the army was infiltrated by the Muslim Brotherhood?"
The assembly is leaning toward a compromise that would allow the military to name the defense minister for one or two presidential terms, al-Shobaki said, speaking on a private TV station.
Another furious debate concerns a 2012 article allowing military trials for civilians for crimes of "harming" the armed forces. The article brought an outcry from rights activists as thousands have been tried by military tribunals, known for swift and harsh verdicts for which there is no appeal.
Some delegates have proposed allowing military trials only in cases where military personnel or facilities are directly attacked.
But others want it out completely. Mossad Aboul-Fagr, an activist on the panel, said he would quit the assembly otherwise.
"It will not pass, and we will not let civilians fall under the mercy of any general," he said.