  We formulate an analogue of the archimedean motivic action conjecture of
Prasanna--Venkatesh for irregular cohomological automorphic forms on Shimura
varieties, which appear on multiple degrees of coherent cohomology of Shimura
varieties. Such multiple appearances are due to many infinity types in a single
$L$-packet with equal minimal $K$-types. Accordingly, we formulate the
conjecture comparing periods of forms of different automorphic representations.
We provide evidences for the conjecture by showing its compatibility with
existing conjectures on periods of automorphic forms. The conjectures suggest
the existence of certain operations which move between different infinity types
in an $L$-packet.
