We propose a simple ansatz that allows us to generate new exactly solvable multistate Landau-Zener models. It is based on a system of two decoupled two-level atoms whose levels vary with time and cross at some moments. Then we consider multiparticle systems with Heisenberg equations for annihilation operators having a similar structure as the Shr\"odinger equation for amplitudes in multistate Landau-Zener models and show that the corresponding Shr\"odinger equation in the multiparticle sector belongs to the multistate Landau-Zener class. This observation allows us to generate new exactly solvable models from already known ones. We discuss possible applications of the new solutions in the problem of the driven charge transport in quantum dots.