We consider stimulated parametric down conversion taking into account higher order multi-particle states generation from spontaneously generated pair of the signal and idler photons. We develop theory of the stimulated emission with both type-I and type-II phase matching in three-mode representation taking into consideration depletion of the pumping mode. Simple representation of output wavefunction of the stimulated parametric down converter is obtained for practical case of very small product of pumping amplitude and gain crystal parameter. We discuss fidelity of the approximation. We apply the multi-particle representation to study influence of the higher order multi-particle states on quantum characteristics (visibility of two-photon coincidence count rate, correlation functions used in Bellรs inequalities) with increase of product of the pumping amplitude and the gain crystal parameter. To expand a possibility to manipulate non-local properties of the two photons we offer a scheme consisting of two down converters with identical responses simultaneously pumped by the pumping mode through the beam splitter. We use first order in the product of the pump amplitude and the gain crystal parameter of the output wavefunction to produce four-path polarizationentangled state that is able to demonstrate violation of the Bellรs inequalities in offered experimental arrangement in the same fashion as for the two-path Bellรs polarization-entangled states.