Abstract: A new variant of the conditional symmetry method for obtaining rank-k solutions of hydrodynamic-type systems in many dimensions is presented. The main idea here is to select the supplementary differential contraints, employed by this method, in such a way that they ensure the existence of solutions expressible in terms of Riemann invariants. These constraints prove to be less restrictive than the conditions required by the generalized method of characteristics and, as a result, one obtains larger classes of solutions. The proposed approach is applied to the fluid dynamic equations in (3+1) dimensions. Several new soliton-like solutions (among them kinks, bumps and multiple wave solutions) are constructed.