  We present an extended framework for hybrid finite element approximations of
self-adjoint, positive definite operators. It covers the cases of primal,
mixed, and ultraweak formulations, both at the continuous and discrete levels,
and gives rise to conforming discretizations. Our framework allows for flexible
continuity restrictions across elements, and includes the extreme cases of
conforming and discontinuous hybrid methods. We illustrate an application of
the framework to the Kirchhoff-Love plate pending model and present three
primal hybrid and two mixed hybrid methods, four of them with numerical
examples. In particular, we present conforming frameworks for (in classical
meaning) non-conforming elements of Morley, Zienkiewicz triangular, and
Hellan-Herrmann-Johnson types.
