  We explore the algebraic properties of a generalized version of the
iterated-sums signature, inspired by previous work of F.~Kir\'aly and
H.~Oberhauser. In particular, we show how to recover the character property of
the associated linear map over the tensor algebra by considering a deformed
quasi-shuffle product of words on the latter. We introduce three non-linear
transformations on iterated-sums signatures, close in spirit to Machine
Learning applications, and show some of their properties.
