Under the new terms, Virgin Money shareholders would own 38 per cent of the new merged business instead of 36 per cent.
CYBG and Virgin Money said the move would create “the UK’s first true national banking competitor” as an alternative to the incumbent banks.
It would be the UK’s fifth largest bank with six million personal and business customers and a balance sheet of £70bn.
CYBG has said it will keep the Virgin Money brand, subject to an agreement with Richard Branson’s Virgin Group.
The proposals would also see improved efficiencies across the business.
Virgin Money, which was founded in 1995, expanded its business in 2011 when it bought the remnants of Northern Rock for about £747m.