Earlier this week, No 10 confirmed a lawyer would investigate two complaints about Mr Raab.
Now it says a new claim relating to Mr Raab's behaviour as Brexit secretary in 2018 will also be examined.
Mr Raab, who is both the justice secretary and deputy prime minister, has denied any allegations of bullying.
He has insisted he "behaved professionally at all times" and that he looks forward to dealing with the complaints "transparently rather than dealing with anonymous comments in the media".
Mr Raab is a close ally of Mr Sunak and Downing Street has said he has the PM's full confidence.
But Labour's deputy leader, Angela Rayner, has called for a wider "proactive investigation" of Mr Raab's behaviour during his time as a minister, covering informal complaints as well as any concerns raised formally.
She described restricting the scope of the investigation to only formal complaints as a "stitch-up" that "will fool no one".
It comes after sources told the BBC the Ministry of Justice, where Mr Raab now works, has been "inundated" with complaints of alleged bullying.
Last week, Mr Raab asked Mr Sunak to launch an inquiry into his conduct after allegations about his behaviour towards staff.
The government appointed lawyer Adam Tolley KC to "establish the specific facts" about two formal complaints that have been lodged about Mr Raab's conduct when he was foreign secretary and justice secretary, during Boris Johnson's premiership.
The lawyer will report to Mr Sunak, who will make the final judgement on whether Mr Raab's conduct breached the ministerial code.
But the scope of the inquiry can be widened "at the discretion of the prime minister, in consultation with the investigator," according to its terms of reference.
Mr Raab was sacked as justice secretary and deputy prime minister by former PM Liz Truss when she took power in September.
But the Esher and Walton MP was reappointed to both roles by Mr Sunak following his election as Conservative leader by the party's MPs.
There is now a coordinated effort by former private secretaries of Mr Raab to ensure their allegations are heard as part of the investigation.
Private secretaries work in the private office of government ministers on the day-to-day running of the department, including managing the minister's diary and advising on policy matters.
The BBC has been told that a number of these civil servants across multiple departments are preparing to submit their formal complaints.
Of these complaints, some have already been submitted formally to government departments, while others are being readied.
They cover a wide timescale, spanning from when Mr Raab was a junior minister to his time in cabinet, which he joined in July 2018 as Brexit secretary.
Labour's deputy leader said: "There must be no hint of a whitewash when it comes to the slew of serious allegations the deputy prime minister now faces."
Liberal Democrat Chief Whip Wendy Chamberlain MP said: "This flood of allegations about Dominic Raab's bullying behaviour cannot be swept under the carpet - Rishi Sunak must confirm he will sack Raab if these complaints are upheld."
Downing Street said the latest formal complaint about Mr Raab was received on Wednesday and Mr Sunak asked for it to become part of the formal investigation on Thursday evening.
Addressing claims of bullying, the deputy PM says he has behaved in line with the ministerial code.