  We contribute to fulfil the long-lasting gap in the understanding of the
spatial search with multiple marked vertices. The theoretical framework is that
of discrete-time quantum walks (QW), \textit{i.e.} local unitary matrices that
drive the evolution of a single particle on the lattice. QW based search
algorithms are well understood when they have to tackle the fundamental problem
of finding only one marked element in a $d-$dimensional grid and it has been
proven they provide a quadratic advantage over classical searching protocols.
However, once we consider to search more than one element, the behaviour of the
algorithm may be affected by the spatial configuration of the marked elements
and even the quantum advantage is no longer guaranteed. Here our main
contribution is threefold~: (i)~we provide \textit{sufficient conditions for
optimality} for a multi-items QWSearch algorithm~; (ii)~we provide analytical
evidences that \textit{almost, but not all} spatial configurations with
multiple marked elements are optimal; and (iii)~we numerically show that the
computational advantage with respect to the classical counterpart is not always
certain and it does depend on the proportion of searched elements over the
total number of grid points.
