  We formulate quantum field theories of massive fields of arbitrary spins. The
presence of both physical and fake particles, organized into multiplets, makes
it possible to fulfill the requirements of locality, unitarity and
renormalizability at the same time. The theories admit cubic and quartic
self-interactions and can be coupled to quantum gravity and gauge fields. The
simplest irreducible bosonic and fermionic multiplets are made of towers of
alternating physical and fake particles. Their mass spectrum is constrained by
RG invariant relations and depends on just one or two masses. The fixed points
of the renormalization-group flow are scale invariant, but not necessarily
conformal invariant. The Palatini version of quantum gravity with fakeons is
equivalent to the non-Palatini one coupled to a peculiar multiplet of order 3.
As a consequence, it is equally renormalizable and unitary.
