Instead of most existing postprocessing schemes, a new preprocessing approach, called multineighboring grids (MNG), is proposed for solving PDE eigen-problems on an existing grid $$\mathbb{G}(\Delta )$$ . The linear or multi-linear element, based on box-splines, are taken as the first stage K 1 h U h = λ 1 h M 1 h U h . In this paper, the j-th stage neighboring-grid scheme is defined as K j h = λ j h M j h U h , where K j h := M j−1 h ⊗ K 1 h and M j h U h is to be found as a better mass distribution over the j-th stage neighboring-grid $$\mathbb{G}(\Delta )$$ , and K j h can be seen as an expansion of K 1 h on the j-th neighboring-grid with respect to the (j − 1)-th mass distribution M j−1 h . It is shown that for an ODE model eigen-problem, the j-th stage scheme with 2j-th order B-spline basis can reach 2j-th order accuracy and even (2j +2)-th order accuracy by perturbing the mass matrix. The argument can be extended to high dimensions with separable variable cases. For Laplace eigen-problems with some 2-D and 3-D structured uniform grids, some 2j-th order schemes are presented for j ⩽ 3.