How to change mirror part way through making object without changing object? I have used the mirror tool in the X and Y axes to create a cone-like surface that is symmetrical in both directions.

Now I want to modify this surface to add details to it that are only symmetrical along the X axis.

When I attempt to make the changes I want now, it mirrors onto all four faces of the shape. If I attempt to remove or change the mirror, it deletes the mirrored parts of the object, which I want to keep.
You have to apply the mirror modifier for the Y axis. To apply a modifier press the the apply button on the modifier. Then you can go back in to edit mode and your details will only be symmetrical along the X axis.