We decribe a new higher-spin particle system which yields some other previously known higher-spin particle models as different gauge choices. The quantization of the new model gives rise to a new form of the massless free higher-spin equations in an extended space also involving, besides extra spinorial twistor-like variables, a complex scalar coordinate. New higher-spin multiplets with a non-zero fixed minimal helicity are obtained. We also discuss a supersymmetric generalization and reformulation in terms of twistors.