  Kaneko and Yamamoto introduced a convoluted variant of multiple zeta values
(MVZs) around 2016. In this paper, we will first establish some explicit
formulas involving these values and their alternating version by using iterated
integrals, which enable us to derive some explicit relations of the multiple
polylogarithm (MPL) functions. Next, we define convoluted multiple $t$-values
and multiple mixed values (MMVs) as level two analogs of convoluted MZVs, and,
similar to convoluted MZVs, use iterated integrals to find some relations of
these level two analogs. We will then consider the parametric MPLs and the
parametric multiple harmonic (star) sums, and extend the Kaneko-Yamamoto's
"integral-series" identity of MZVs to MPLs and MMVs. Finally, we will study
multiple integrals of MPLs and MMVs by generalizing Yamamoto's graphical
representations to multiple-labeled posets.
