Yes, either with a correction deformer, should you need the SDS to remain parametric, which does limit component operations to mainly selections only, or, as mentioned in first post, you can APPLY the current subdivision by hitting C with the SDS object selected rather than the base model which is under it. Note the level of subdivision that gets applied is the RENDER SD value, not the viewport level.
Making SDS editable (usually only one Level of it at a time ) is a valid and valuable technique for increasing the level of subdivision evenly all over a mesh, which is sometimes more helpful than having to add specific loops to the base mesh, which is preferable in most cases only if you need additional loop detail / density in one particular area and not spread across the whole mesh.
Here is your fish with various levels of SD applied - at the top no SD, then L1, then L2.
A valuable note on this technique is that your total level of applied subdivision shouldn't ever total more than 3, unless you are using SDS edge weighting in which case the sensible maximum is L4 or 5. So if you apply 1 level of subdivision to a base mesh, and then put that mesh inside a another live SDS, then the live SDS should only have a maximum of L2 because you have already applied one level, if that makes sense.
CBR