A Keighley supermarket is planning to extend.
Aldi is seeking to build on to the southern elevation of its Gresley Road store.
The scheme would see floorspace increase by almost a quarter, from 765 to 960 square metres, and the store entrance would be moved.
Six car-parking spaces at the site would be lost.
The plans have been submitted to Bradford Council at the same time rival company Asda awaits a decision on design issues relating to its proposed new superstore.
Outline permission has already been given for the Asda store, to be built in Bradford Street. It is due to open next year.
Aldi opened its first UK store in 1990 and now has more than 300 across Britain.
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