  We present a systematic technique to construct solutions to the Yang-Baxter
equation which depend not only on a spectral parameter but in addition on
further continuous parameters. These extra parameters enter the Yang-Baxter
equation in a similar way to the spectral parameter but in a non-additive form.
We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$
and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are
known to admit non-trivial one-parameter families of infinite-dimensional and
finite dimensional irreps, respectively, even for generic $q$. We develop a
technique for constructing the corresponding spectral-dependent R-matrices. As
examples we work out the the $R$-matrices for the three quantum algebras
mentioned above in certain representations.
