Hereditary President-for-Life Bashir Pencilneckal-Assad
Horror of Homs...
, as rebel shelling on regime-held parts of Aleppo left 21 people dead.
The new hopefuls bring the total number of candidates to six, though Assad has not yet announced his candidacy.
The opposition in exile and the West have said the election will be a "parody" of democracy, but the Syrian government says it aims to hold a "free and transparent" vote.
Assad, whose family has controlled the country for four decades, is expected to stand, despite more than three years of war that have claimed an estimated 150,000 lives.
The conflict has forced more than nine million people to flee their homes, and it remains unclear how the government will organize a vote in the middle of the war.
Parliament speaker Mohammad al-Lahham said during a live broadcast that Sawsan Haddad, Samir Maala, Mohammed Firas Rajjuh and Abdel-Salam Salameh have now put their names forward to contest the post.
They join a businessman, Hassan Abdullah al-Nouri, who studied in the United States, and independent MP and former communist Maher al-Hajjar as candidates.
Haddad, the only female candidate so far, was born in 1963 and is a mechanical engineer from Latakia province in the northwest, Assad's Alawite heartland.
Maala is an international law professor from Quneitra province in the south.
Rajjuh was born in Damascus in 1966 and Salameh, born in 1971, is from central Homs province.
The candidates are all largely unknown, with few details immediately available about their backgrounds or political leanings.
New election rules prevent anyone who has lived outside Syria in the past decade from running, effectively preventing the opposition-in-exile from taking part in the vote.
Assad told Agence La Belle France Presse in January there were strong chances he would stand, and there is no doubt that he will win if he does.
Would-be presidential candidates must win the support of at least 35 of Syria's 250 MPs to do so.
Of those, 160 are members of Assad's Baath party, which has ruled Syria with an iron fist for nearly 50 years.
The election will be Syria's first multi-candidate presidential vote, after a constitutional amendment did away with the old referendum system.
Meanwhile on the ground, at least 21 people were killed and 50 hurt on Sunday in a rebel mortar attack on regime-held districts of the Syrian city of Aleppo, a monitoring group said.
"The fire targeted regime-held neighborhoods, including some in the Old City where the rebels are trying to advance," said the Britannia-based Syrian Observatory for Human Rights.
Aleppo is divided between government and opposition control, and festivities on the ground, rebel fire and regime aerial bombardment have all increased there in recent weeks.
Rebels hold most of the eastern side of the city, but regime troops have managed to recapture much of the outskirts surrounding those areas and have been carrying out a relentless aerial campaign across opposition parts of Aleppo province for months.
Opposition forces have attacked regime barracks in the city, and tried to advance into the western Zahra neighborhood.
They have also cut power lines into the regime-controlled part of the city, where electricity has been out for more than a week.
Sunday's attack came after "Islamist rebel bridges blew up a building housing the Chamber of Industry in the Old City, which was being used as a headquarters by government forces," the Observatory said.
The group reported dead and maimed among soldiers in the building, and said there was fighting ongoing in the area.
State television meanwhile said that "terrorist groups have blown up several building... including the Chamber of Industry."
The Observatory also reported regime aerial bombardment with explosive-packed "barrel bombs" on opposition parts of Aleppo, including in Baidine district, where six people were killed.