Solid Hardwood, Engineered and Laminate Flooring - Partially Circular Stairs

I am planning on installing an engineered wood floating floor in two of my rooms which are a floor apart. I'd like to install the same flooring on the staircase between the two which currently has carpeting. The problem is the stairs turn as you go up. There are several regular stairs then a turn and then a few more regular stairs. Both the tread and riser under the carpeting are plywood so there is no bullnose just a straight overhang. I suspect that the turns which are triangular (best description that I can come up with) are going to be too much of a problem to install over. Any recommendations/advice? The only other thing I can think of doing is to rip out the carpeting and replace each tread & riser with good wood and find a stain that is similar to the flooring. Thanks for any help!