Sandpiper has revised its application to take over Jersey's Costcutter stores.
The company wanted to buy all sixteen shops, but the competition regulator refused that.
They said the proposed acquisition as it stood had the "potential to harm consumer interests", reducing competition in particular in island grocery stores.
Now Sanpiper hope to buy thirteen of the shops instead, excluding the ones at St Ouen, St John and Green Island.
They plan to convert them into brands already in their portfolio including Iceland and Foodhalls.
Sandpiper is the largest high street operator and works as a franchise group for shops including Marks & Spencer, Iceland and Burger King.
The merger will be considered by the Channel Islands Competition and Regulatory Authority (CICRA).
CICRA chief executive, Michael Byrne said:
The deal is subject to regulator approval.