Leeds and Burnley have asked the Premier League to order Everton not to delete any data or communication relating to their commercial, sponsorship or transfer business.
The two clubs are stepping up their attempts to get Everton's financial accounts independently investigated.
Both have written to the league about the Toffees' latest accounts, which show losses of £120.9m for 2020-21.
Everton have posted losses of £372m over the past three years.
League profitability and sustainability rules allow for losses of £105m over a three-year period but Everton say Covid-19 losses over the past two seasons amount to £170m, which can be deducted from their total.