The joint venture of T-Mobile and Orange has announced a major press event tomorrow morning in London, at which it will share "exciting information on our new brand and the latest innovation in network technology".
It is thought that this will include the unveiling of an already confirmed third brand in the firm's stable, which will be a new premium label offering 4G mobile phones and mobile broadband dongles.
The timing of the event, just a day ahead of a major Apple press event on Wednesday (September 12), has raised speculation that Everything Everywhere could offer a rumoured 4G version of the iPhone 5.
Last month, Everything Everywhere was controversially given permission by Ofcom to reuse some of its 1800Mhz spectrum to offer 4G services in Britain from September 12.
It was initially thought that Everything Everywhere would only be able to offer 4G in a small area of the UK, but The Daily Telegraph's sources claim that the early rollout will actually be much wider.
It is thought possible that Nokia's new Lumia smartphones will be offered by Everything Everywhere's new 4G brand, although these handsets are not expected to actually go on sale until November.
On Wednesday, Apple is thought likely to announce a 'pentaband' iPhone 5, meaning it can pick up five different radio frequencies.
Getting exclusivity on the 4G iPhone would give Everything Everywhere a major advantage, as users of the handset would benefit from mobile broadband speeds of up to 100Mbps, compared to just 5Mpbs.
However, the question remains whether Everything Everywhere had enough time to persuade Apple to include its adapted 1800MHz spectrum for 4G in the iPhone 5 frequencies, particularly as it only received Ofcom approval last month.
Another issue is the threat of a legal challenge from rival operators such as O2 against Ofcom's decision to allow Everything Everywhere to reuse its spectrum.
Rival mobile operators are concerned that it gives the firm a major competitive advantage ahead of a planned auction of spectrum for the wider launch of 4G mobile next year.
But Everything Everywhere has in turn warned that any legal challenges to its current 4G plans would potentially result in the firm launching its own challenge to the terms of the auction.