Image copyright AFP Image caption Sexual harassment scandals have rocked Fox News - and led to some top-level departures

The ancient adage was never wrong, and thanks to Fox News we can now offer an update: to lose one may be considered a misfortune; to lose two is a sign something's up; but to lose three is a sign that something is rotten in America's most watched news network.

The sacking of ratings juggernaut Bill O'Reilly last month was the most significant departure in the modern history of American cable news. Except that is, for the departure of his boss Roger Ailes last year.

These two monumental media events - the first, a dismissal of the biggest talent on America's most influential news service; the second, a dismissal of the most influential man in American news media (after his boss, Rupert Murdoch) - have now been followed by another remarkable departure: that of Bill Shine, who ran Fox News with Ailes for two decades, and was appointed co-president to sort the mess out.

Three huge departures within nine months. There is now chatter that Sean Hannity, the senior anchor who tweeted last week that Fox News would be finished without Shine, could be the next to go.

What is going on? And could this affect UK communications regulator Ofcom's forthcoming judgement on whether to reject the Murdoch family's bid for the 61% of broadcaster Sky they don't own?

Echoes of hacking scandal

That is certainly the hope of the cross-party group of MPs who have been lobbying Ofcom, and who would rather not see the Murdochs consolidate their power here in the UK. Interestingly, former business secretary Sir Vince Cable said on BBC Radio 4's World at One that Ofcom told him they were in listening mode. And there is certainly a lot of noise emanating from Fox News HQ in Manhattan right now.

There is a palpable fear in New York that the sexual harassment scandal which has toppled Roger Ailes and Bill O'Reilly could be an American version of the phone hacking scandal that dogged Rupert Murdoch's British newspapers. The echoes are eerie.

Image copyright Getty Images Image caption Roger Ailes - Is he just one rogue individual?

First, there is the instinctive blame on one rogue individual. Fox insiders have generally blamed the dominant, strongman personality of Roger Ailes for what went wrong, saying that with his departure the culture would improve. This sounds familiar to those who remember the initial claim that phone hacking was conducted by "one rogue reporter".

Second, there are the wider questions about a corporate culture. I don't mean by this whether or not Fox News leans to the right. I mean whether or not it is well run. Shine, who we're told resigned over the weekend, wasn't accused of sexual or racial harassment himself; but he was accused by multiple individuals of knowing plenty about the behaviour of his boss, and failing to act appropriately.

Third, and related, there are the legal investigations now under way: not one, but two. The bigger one is a federal probe looking at whether or not Fox withheld settlement payments over sexual harassment from investors.

And fourth, and worst of all for the Murdochs, there is the time. The phone hacking scandal derailed their last attempt to acquire the part of Sky which they don't already own. Now, with Ofcom's assessment of their latest takeover bid in the long grass until after the UK general election on 8 June, this huge scandal threatens to generate all the wrong headlines. The timing couldn't be worse.

For all that, it is important to note that Fox's ratings haven't suffered, and the advertising boycott that followed the revelations around O'Reilly - who strenuously denies he's done anything wrong, and is now forging a fresh career as a podcaster - hasn't yet dented Fox revenues in a really significant way.

Image copyright AFP Image caption The Murdochs' last takeover bid for Sky was derailed by the phone hacking scandal

Moreover, Fox has moved swiftly and decisively in removing toxic individuals, in a way that shows they are extremely alert to potential reputational and commercial damage. It really was unimaginable this time last year that Fox News could exist without Ailes, let alone O'Reilly and even Megyn Kelly, who is probably America's most sought after female anchor, and left the network a few months ago.

The dominant narrative in American media is that these moves show Rupert's sons, James and Lachlan, imposing their worldview on their father's media giant by decisively rejecting the orthodoxies of his reign.

A new broom?

In conversations with seasoned observers of Planet Murdoch, individuals at 21st Century Fox, and opponents of that company's bid for the 61% of Sky it doesn't already own, that narrative finds plenty of support.

That both Ailes and O'Reilly have gone does give credence to the idea that Fox News is being reconfigured by its parent company, 21st Century Fox, where Executive Chairman Lachlan, and CEO James - who are of equal status - want change. Since they acquired this joint status in June 2015, these two have made a concerted effort to modernise their father's firm.

They have held regular town hall meetings with staff, extended parental leave, and made a habit of sending memos to staff - whether groups or individuals - saying well done: a pillar of right-on modern management.

More importantly, they have appointed several women to key roles, from Stacey Snider (in charge of 20th Century Fox film studio) to Courteney Monroe (CEO of National Geographic, a particular passion for James). The entertainment division of 21st Century Fox has several women in key executive roles, from Elizabeth Gabler and Nancy Utley to Emma Watts and Vanessa Morrison.

Image copyright Getty Images Image caption Rupert Murdoch still rules the roost - but his sons have moved to modernise the family business

Fox insiders are frustrated that the strides made in equality in the entertainment division garner much less publicity than the misdeeds of senior men in the (much smaller and less profitable) news division.

With commercial titans like Chase Carey, Peter Chernin, and now Ailes out of the picture, and James and Lachlan in the ascendant, there is a sense of a new broom at the company.

NYT takedown

But Rupert still rules the roost. I would urge caution on those who argue that his grip is weakening. Not only was he, as you'd expect, ultimately responsible for the decisions to remove Ailes, Shine and O'Reilly; not only did he install himself as the temporary but very hands-on chairman of Fox News after Ailes left; but the idea that there was a battle of wills between father and sons, who outnumbered and outfoxed their father, is fanciful.

It is worth bearing in mind how much Rupert would have hated the New York Times felling of O'Reilly. It was their brilliant investigation that revealed the payments made to complainants against O'Reilly, causing a boycott by dozens of advertisers. Murdoch senior coveted the Grey Lady for many years, and paid a huge price for the Wall Street Journal partly because he was so determined to get one over it. The New York Times is the very embodiment of the liberal coastal elite O'Reilly, Shine and Ailes have spent decades bashing. The irony is not lost on either party.

What next for Fox News? Hannity's future remains unclear. Former UK Independence Party leader Nigel Farage, who works for Fox News, told me a fortnight ago that Tucker Carlson, the anchor who has replaced O'Reilly in the key 8pm slot, has long been thought of as his likely successor. In his first few days, Carlson has rated well.

But the bigger drama is yet to come: the federal probes into whether payments were withheld from investors could intensify just as Ofcom consider whether to approve the Murdochs' bid for Sky. The last bid was of course derailed by the phone hacking scandal; and while Ofcom won't comment on what is a quasi-judicial process, their deliberations aren't taking place in a vacuum.

In ancient times, before Donald Trump was elected and when some people naively believed Hillary Clinton would be US president, the mood music coming out of New York suggested that the sons would build Fox News around Megyn Kelly, taking it in a more centrist and female-friendly direction. Now she's gone, and Rupert Murdoch is trying to rid his network of the cancer threatening to spread through it.

Suddenly, the future of Fox News is up for grabs - and British regulators are watching.