  We complete the set of spin-projector operators for fields up to rank-3 by
providing all operators connecting sectors with same spin and parity. In this
way we can broaden the search for unitary and non-tachyonic particle
propagation in quadratic lagrangian with inter-field mixing. We use the
properties of projector algebra to reanalyze known theories and shed light
towards new healthy ones. We do so with full control over the gauge constraints
by working the form of the saturated propagator in an appropriate frame of
reference.
