  In this work we address the problem of finding serendipity versions of
approximate de Rham complexes with enhanced regularity. The starting point is a
new abstract construction of general scope which, given three complexes linked
by extension and reduction maps, generates a fourth complex with cohomology
isomorphic to the former three. This construction is used to devise new
serendipity versions of rot-rot and Stokes complexes derived in the Discrete de
Rham spirit.
