A ruling against the pact could leave the country facing a fourth poll.
Under the proposed three-year agreement between Prime Minister Benjamin Netanyahu and his rival-turned-partner Benny Gantz, each would head the government for a period of 18 months.
But eight separate petitions to the court seek to declare the deal illegal, including one from former Gantz ally Yair Lapid, head of the opposition Yesh Atid.
On Sunday, the court spent seven hours hearing other challenges to another Netanyahu term as premier, based on the fact that he is facing a criminal trial on corruption charges.
Some commentators see that tactic as unlikely to succeed in light of a legal opinion from Attorney General Avichai Mandelblit that there is no legal basis to prohibit him from taking office.
Mandelblit has however advised that "certain arrangements in the coalition agreement raise major difficulties," although he said there are not grounds to throw out the whole accord.
"Today… the court will dive into the details of the coalition agreement - and this is where the decision that will bring about a fourth election could be made," Tova Tzimuki wrote Monday in top-selling Israeli daily Yediot Aharonot.
"The disqualification of any one section of the agreement... will cause the unprecedented legal construction on which it is supposed to be based to wobble," she added.
The arguments are being heard by a panel of 11 judges, sitting in facemasks and divided by perspex panels as part of measures to prevent the spread of the novel coronavirus.
Proceedings are being streamed live on the court's website.
A ruling is expected by Thursday, the deadline for forming a government under electoral law.
The veteran premier has been charged with accepting improper gifts and illegally trading favours in exchange for positive media coverage. He denies wrongdoing and his trial is set to start May 24.
Israeli law bars an indicted person from serving as an ordinary cabinet minister, but does not compel a criminally-charged prime minister to leave office.
Read also: The Netanyahu-Gantz coalition farce
The deal
The main argument against the coalition deal concerns specific provisions that opponents say violate the law.
The agreement sees Netanyahu serving as prime minister for 18 months, with Gantz as his "alternate", a new title in Israeli governance.
They will swap roles midway through the deal before likely taking voters back to the polls in 36 months.
But Israeli law traditionally endows governments with four-year terms, an issue pounced on by the deal's opponents.
There is also a provision freezing certain public appointments during the government's initial six-month pandemic emergency phase, which critics also say is illegal.
Mandelblit, who indicted Netanyahu, has recommended that problematic provisions be reviewed "at the implementation stage".
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