Downing Street has expanded the inquiry into alleged bullying by Dominic Raab to include a third formal complaint, relating to claims about his behaviour in a third ministerial role. The investigation, by the senior employment barrister Adam Tolley KC, who was appointed by Rishi Sunak on Wednesday to look into allegations about the deputy prime minister, will now examine a complaint relating to his four-month stint as Brexit secretary in 2018. Tolley was already dealing with complaints against Raab, who is also the justice secretary, made by officials at the Ministry of Justice and the Foreign Office, where he served as foreign secretary. Sunak’s deputy spokesperson said: “I can confirm that the prime minister has now asked the investigator to add a further formal complaint relating to conduct at the Department for Exiting the European Union, and to establish the facts in line with the existing terms of reference.” The third complaint was received by the Cabinet Office on Wednesday, she said. “That was looked at. The prime minister was provided with advice from the Cabinet Office, and last night he asked for the scope to be updated.” Raab has denied bullying, and vowed to “thoroughly rebut and refute” the allegations. The spokesperson said Sunak had confidence in Raab and would not be providing “a running commentary” while the inquiry took place. “As we’ve said, there is now an independent investigation ongoing. It’s led by someone with extensive experience in this area. We’re not going to pre-empt or prejudge that process,” she said. The Guardian has revealed multiple allegations of bullying and intimidatory behaviour by Raab across three government departments – the MoJ, the Brexit department and the Foreign Office. Sunak has faced questions over his judgment in reappointing him as they came to light. Labour has called on Sunak to expand the scope of the inquiry to allow the proactive and independent investigation of formal and informal complaints about Raab’s alleged behaviour. Earlier this week, the Guardian reported that Raab allegedly behaved so badly in a meeting with the Home Office during his first stint as justice secretary – he held the job under Boris Johnson, but was removed during Liz Truss’s seven weeks as PM – that his department’s top official had to personally apologise to counterparts afterwards. Whitehall sources said Raab acted “so badly and inappropriately” at a high-level meeting earlier this year that the permanent secretary at the MoJ was forced to call senior officials of the then home secretary, Priti Patel, to express regret.