  We introduce and study the notion of space of almost universal complemented
disposition (a.u.c.d.) as a generalization of Kadec space. We show that every
Banach space with separable dual is isometrically contained as a
$1$-complemented subspace of a separable a.u.c.d. space and that all a.u.c.d.
spaces with $1$-FDD are isometric and contain isometric $1$-complemented copies
of every separable Banach space with $1$-FDD. We then study spaces of universal
complemented disposition (u.c.d.) and provide different constructions for such
spaces. We also consider spaces of u.c.d. with respect to separable spaces.
