In principle your perfect solar-harvesting multi-mirror structure would cover the entire collection area with perfectly flat mirrors, each of such a size and shape that its reflected patch of light would as nearly as possible cover the absorption area of the target throughout the sunlit period each day.It might happen that the mirrors are on rails, and move during the day to continually optimise their yield, but I suspect that just tilting the mirror as the sun moves would be adequate.
On any given time of any given day this would place each mirror on the surface of a paraboloid with the target at the focus for as long as the sun shone clearly enough to be useful. However, with the exception of such mirrors as happened to lie on coinciding arcs sharing the surfaces of the same paraboloids, they would all lie on different paraboloids.
What I have described has nothing to do with designing mirrors to lie on paraboloids; they would do so automatically as a result of reflecting sunlight at the same target. You could set down a lot of school children with mirrors and show each how to direct his mirror at the target, and you still would get the same type of effect. In principle in fact, by choosing a smaller and smaller target, and choosing mirrors smaller and smaller to match, aiming each new split segment more precisely, you could progressively approximate a parabola or paraboloid as closely as you choose.
As for designing the mirrors themselves to be paraboloidal, there is no point as long as no mirror reflects a spot of light larger than the target area. If you prefer to use larger mirrors, then you might consider a paraboloidal contour, or a more sophisitcated shape to deal with special considerations, but I cannot believe that it would be worth it for realistic power harvesting applications. It might be worth it for solar furnaces heating smaller targets to high temperatures, of course.
Oh, and BTW, just a reminder: a parabola is a curved line representing a particular mathematical function. Useless for reflection. A paraboloid is the shape you get if you rotate the parabola around its axis of symmetry, creating a bowl-shaped surface, the shape of a searchlight reflector or the reflector of a paraboloidal telescope.
