Matalan applied for permission for a cafe unit at the St Thomas Street entrance side of its store earlier this year.
It has now lodged a second, separate application to allow an area of outside seating, also in St Thomas Street, for the cafe.
As part of its original application, which is still waiting for approval, the company included a recent appeal decision from Grimsby in which the planning inspectorate overturned a council decision to refuse a Next store permission to open a cafe as part of its supporting evidence.
There is no indication as to how many people could be served by the cafe if it were to get planning permission.
One person has objected to the plans saying there are enough cafes in the area and “the inevitable smells from the cafe could impact on the clothing they sell”.