Again, according to Innes Ferguson, TfL's medium-term aspiration is for the former to be expanded to cover other National Rail services in London and the South-East, either by direct TfL operation through a concession-holder (as with the ex-Silverlink routes) or by a TOC agreeing to operate under the London Overground "brand".
Innes Ferguson asserts that TfL intends to extend the former service to encompass additional National Rail routes in London and the South-East. This might involve direct operation via a concession-holder, akin to Silverlink, or through a TOC operating under the London Overground brand.