  Multi-photon states can be produced in multiple parametric down conversion
(PDC) processes. The nonlinear crystal in such a case is pumped with high
power. In theory, the more populated these states are, the deeper is the
conflict with local realistic description. However, the interference contrast
in multi-photon PDC experiments can be quite low for high pumping. We show how
the contrast can be improved. The idea employs currently accessible optical
devices, the multiport beam splitters. They are capable of splitting the
incoming light in one input mode to $M$ output modes. Our scheme works as a
POVM filter. It may provide a feasible CHSH-Bell inequality test, and thus can
be useful in e.g. schemes reducing communication complexity.
