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We complete the set of spin-projector operators for fields up to rank-3 byproviding all operators connecting sectors with same spin and parity. In thisway we can broaden the search for unitary and non-tachyonic particlepropagation in quadratic lagrangian with inter-field mixing. We use theproperties of projector algebra to reanalyze known theories and shed lighttowards new healthy ones. We do so with full control over the gauge constraintsby working the form of the saturated propagator in an appropriate frame ofreference.

Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories