Water coming in between the floor and icf walls

I am assuming that you are correctly diagnosing they fact that the water is rising from below the slab and not coming through the wall.

If you have the proper gravel base under the new floor, adding another sump might allow the water to travel through the gravel to the sump instead of rising at the joint.

And added step you can take is to channel any water that does rise to the new sump which should be located at the lowest point of the floor.

As a DIY project you are only risking a couple of hundred dollars.

What is an ICF wall??????

You won't know unless you do it. Odds are in your favor. Do some thinking about the terrain and drainage and locate the sump pit closest to where you suspect the source might be, like the uphill side of the house if the lot is bit unlevel. Do whatever is needed to correct downspouts and grading, too.

Joe

I had to look it up myself. Insulated concrete form. Think insulated concrete blocks that are then filled with concrete and that will be close enough.