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The Metropolitan Police said the allegations were all non-recent.
A statement said: "Following an investigation by Channel 4's Dispatches and The Sunday Times, the Met has received a number of allegations of sexual offences in London.
"We have also received a number of allegations of sexual offences committed elsewhere in the country and will investigate these."
There have been no arrests and enquiries continue.
Last Monday, the Met said it had received one report of alleged sexual assault from 2003 and encouraged other potential victims to come forward.
Brand denies all the allegations against him, says his relationships were consensual, and has not been charged with anything.
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He has admitted being very promiscuous in the past, but called the reports "very serious allegations that I absolutely refute".
In a video last week on YouTube - which has cut off his advertising revenue - he said it had been a "distressing" time.
Brand appeared on video platform Rumble on Monday and criticised an MPs' committee for asking other social media firms if they intended to demonetise him.
He called it a "bypassing of judicial process" and suggested there was a conspiracy to silence him and "independent media voices".
Brand told viewers: "What we appear to be looking at here are a set of collaborating institutions that have an agenda, and pursue that agenda, even when in pursuing it they have to bypass, obstruct, or absolutely ignoring existing judicial or regulatory bodies by moving straight to punitive measures."
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The claims against the 48-year-old include an allegation of rape, and that he sexually assaulted a 16-year-old girl he was seeing.
Another woman told Sky News he made her feel "vulnerable and intimidated" and alleged he refused to call her a taxi until she performed a sex act.
The fallout from the claims has caused Brand to suspend his tour, as well as reigniting a debate about how stars are managed and monitored by the entertainment industry.