  The established approach of perturbative continuous unitary transformations
(pCUTs) constructs effective quantum many-body Hamiltonians as perturbative
series that conserve the number of one quasiparticle type. We extend the pCUT
method to similarity transformations - dubbed $\mathrm{pcst}^{\texttt{++}}$ -
allowing for multiple quasiparticle types with complex-valued energies. This
enlarges the field of application to closed and open quantum many-body systems
with unperturbed operators corresponding to arbitrary superimposed ladder
spectra. To this end, a generalized counting operator is combined with the
quasiparticle generator for open quantum systems recently introduced by
Schmiedinghoff and Uhrig (arXiv:2203.15532). The $\mathrm{pcst}^{\texttt{++}}$
then yields model-independent block-diagonal effective Hamiltonians and
Lindbladians allowing a linked-cluster expansion in the thermodynamic limit
similar to the conventional pCUT method. We illustrate the application of the
$\mathrm{pcst}^{\texttt{++}}$ method by discussing representative closed, open,
and non-Hermitian quantum systems.
