Ok.
Imagine a shoe like the Metcon. If you've tried them on, they stick to te ground really damn well. They have a base that protrudes outward onto the ground, reminiscent of the other shows. This is the base.
Now here where you get creative. I recently bought clipless pedals for my bike so I'm a little inspired by mechanical solutions. Imagine the shoe has a magnet system. A magnet embedded into the heel of the shoe. With a little box shaped hole were one can place the sole with a perfectly shaped magnet to fit in that hole. In other words, this shoe comes with two soles: one for everyday function and a plastic hole cover to insert in that magnet, and a "oly" sole with a magnet that fits in that hole. Hell, you could place smaller weaker magnets on the sides of tr heel area to help keep the sole in place.
In this way, we have an elevated sole with super secure magnets keeping it in place and a show that has tr properties of the other shoes. The shoes could have those Velcro straps too.
Anyway, that's just a first attempt. I can imagine having more tools at my disposal. My gut doesn't see a problem with something like this.