  Kustin--Miller unprojection constructs more complicated Gorenstein rings from
simpler ones. Geometrically, it inverts certain projections, and appears in the
constructions of explicit birational geometry. However, it is often desirable
to perform not only one but a series of unprojections. The main aim of the
present paper is to develop a theory, which we call parallel Kustin--Miller
unprojection, that applies when all the unprojection ideals of a series of
unprojections correspond to ideals already present in the initial ring. As an
application of the theory, we explicitly construct 7 families of Calabi--Yau
3-folds of high codimensions.
