Changing interface signature without editing code in multiple places

[NiceStepUp]

I have an interface and existing code which implements this interface:

public interface IBusinessService<T> where T : class
{
Task Add(T category);

Task Delete(T category);

Task Update(T category);

Task<IEnumerable<T>> GetAll();

Task<T> GetById(int id);
}

Now some id has type of Guid. So I cannot use this method to send Guid id:

var id = Guid.NewGuid()
GetById(id);

So we need that id parameter can be type of Guid. It would be ideal if it is possible:

public interface IBusinessService<T> where T : class
{
/* ... the other code is omitted for the brevity */
Task<T> GetById(Guid or int id );
}

What I thought to implement is to create a new method with parameter type of Guid:

public interface IBusinessService<T> where T : class
{
Task Add(T category);

Task Delete(T category);

Task Update(T category);

Task<IEnumerable<T>> GetAll();

Task<T> GetById(int id);

Task<T> GetById(Guid id);
}

But if I will do this, then I need to edit so many code. So it looks like it is not a good solution.

Is there a way to add another type of id to the interface method GetById without breaking changes?

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