Another way you can control the returned result set will be adding an additional parameter which will decied how many and which result sets are returned when a stored procedure is called.
For example in your [Existing_StoredProcedure]
you can do something like .....
ALTER PROCEDURE [Existing_StoredProcedure]
@a VARCHAR(10),
@b VARCHAR(10),
@c VARCHAR(10),
@ResultSet INT = NULL --<-- Indicator Param
AS
BEGIN
SET NOCOUNT ON;
-- Common code that executes regardless of what result set is required
-- Now return the result set based on value passed to @ResultSet
IF (@ResultSet = 1 OR @ResultSet IS NULL)
BEGIN
-- Code for 1st result set
END
IF (@ResultSet = 2 OR @ResultSet IS NULL)
BEGIN
-- Code for 2nd result set
END
END
Now if you dont pass any value to @ResultSet
param both result sets will be returned but if you pass 1 or 2 , only relative result set will be returned.