Hossam Bahgat and Soha Abdelaty of EIPR have an important WaPo op-ed about the constitutional constraints around Mubarak's resignation from the presidency:
So before Mubarak resigns he must sign a presidential decree delegating all of his authorities to his vice president until their current terms end in September. Mubarak issued similar decrees, transferring his powers to the prime minister, when he was hospitalized in 2004 and 2009. In addition, Mubarak must issue decrees lifting the "state of emergency" that has allowed him to suppress Egyptians' civil liberties since 1981 and ordering the release or trial of those held in administrative detention without charge - estimated to be in the thousands.
Also before Mubarak resigns, an independent commission of respected judges, constitutional law experts, civil society representatives and all political movements should draft language to amend the constitution to ensure that presidential elections are open to all credible candidates; that Egyptians abroad are allowed - for the first time - to vote; that any elected president is allowed to serve only two terms; and that the elections are supervised by judicial and civil monitors. Most of this will be a matter of undoing the damage Mubarak inflicted with his constitutional changes in 2007.
These amendments must be introduced in parliament and put to a public referendum immediately. Suleiman's claim that time is short is unfounded and disingenuous; four years ago, Mubarak and his ruling party amended 34 articles of the constitution in only two months.
Next, a diverse caretaker government must be appointed to serve the people until a president is elected and, importantly, to oversee the interim president. This broad-based cabinet must include well-respected representatives of all the country's political forces. Once a new president is elected, we can move toward drafting a constitution that ensures Egypt's transformation from a dictatorship to a democracy and enshrines full equality and human rights. Free and fair parliamentary elections would follow.
Three additional elements are key for the transition to succeed: First, civilian oversight of the police and security forces will deter abuse, hold abusers accountable, and help ensure the safety of those participating in the democratic uprising. Second, establishing an independent board of trustees for state television and radio would ensure neutrality in programming and representation of all political views. Third, a strong commitment by the army to act as a neutral custodian of the transition, serving the interests of the people and not the delegitimized regime, is critical.
Egyptians have paid a heavy price the past three decades and an even steeper one since this revolution started. Let's end Mubarak's rule the right way so we can start building a better future.
To be honest, while the path they highlight is clear and worth considering, I believe extra-constitutional means deserve to be considered to: suspend the current constitution and have a transition council, for instance.
Another path that would remain within the constitution is to use Article 139 to appoint more vice-presidents, each empowered to deal with various aspects of the situation: one to take the lead on constitutional reform, one to investigate the events of the past week, one to restore and reform the Ministry of Interior, etc. It would be a defacto Council of Wise Men (and hopefully at least one woman!)