  In \cite{Mor}, Marcantognini and Mor\'{a}n obtained Koplienko-Neidhardt trace
formula for pairs of contractions and pairs of maximal dissipative operators
via multiplicative path. In this article, we prove the existence of
higher-order spectral shift functions for pairs of contractions and pairs of
maximal dissipative operators via multiplicative path by adapting the argument
employed in \cite{Mor}.
