Grand Central, which operates services from Brighouse and Halifax to London, has begun consultation with other train companies and the infrastructure operator Network Rail to operate more trains per day.
The new services would run on its current routes as well as offer new direct journey opportunities for passengers travelling to and from Peterborough.
Following consultation, the application will be submitted to the Office of Rail and Road (ORR) for consideration.
If approved, the move will bring Grand Central’s current daily North East route operation to six return services, currently five, and its West Yorkshire route would see six trains to London and five returning from London, currently four.
Richard McClean, managing director of Grand Central, said: “The proposed additional services are an important part of Grand Central’s longer term strategic development, building on the strong growth we have seen on our existing routes. We believe that expanding our operations will benefit both our existing and potential new passengers, as well as grow existing markets.”