  Nonlinear phenomena of lepton-photon interactions in external backgrounds
with a generalised periodic plane-wave geometry are studied. We discuss
nonlinear Compton scattering in head-on lepton-photon collisions extended
properly to beyond the soft-photon regime. In addition, our results are applied
to stimulated lepton-antilepton pair production in photon collisions with
unrestricted energies. Derivations are considered semi-classically based on
unperturbed fermionic Volkov representations encoding the full interaction with
the background field. Closed expressions for total probabilities considering
S-matrix elements have been derived. The general formula is applied to Compton
scattering by an electron propagating in an external laser-like background. We
obtain additive contributions in the extended unconstrained result which turns
out to be stringently required in the highly nonlinear regime. A detailed
comparison of contributing harmonics is discussed for various field parameters.
