Duplicating rows but incrementing the ID each time
If the id column has the AUTO_INCREMENT property, then it's pretty straight-forward. Don't include it in the insert list:

INSERT INTO tableX (store_id, column3, column4, ...)
SELECT 2, column3, column4, ...
FROM tableX
WHERE store_id = 1 ; 


This will insert as many rows as there are with id = 1.



If you want to do this for multiple store_id values (not only for 2), i.e. for example for 10 store ids, inserting 10N rows where N is the number of rows with id = 1, you can extend to:

INSERT INTO tableX (store_id, column3, column4, ...)
SELECT s.store_id, t.column3, t.column4, ...
FROM tableX AS t
  CROSS JOIN 
    ( SELECT 2 AS store_id UNION ALL
      SELECT 3 UNION ALL
      ---
      SELECT 11
    ) AS s
 WHERE t.store_id = 1 ;