  In this paper we continue our classification of regular solutions of the
Yang-Baxter equation using the method based on the spin chain boost operator
developed in \cite{deLeeuw:2019zsi}. We provide details on how to find all
non-difference form solutions and apply our method to spin chains with local
Hilbert space of dimensions two, three and four. We classify all $16\times 16$
solutions which exhibit $\mathfrak{su}(2)\oplus \mathfrak{su}(2)$ symmetry,
which include the one-dimensional Hubbard model and the $S$-matrix of the ${\rm
AdS}_5 \times {\rm S}^5$ superstring sigma model. In all cases we find
interesting novel solutions of the Yang-Baxter equation.
