  We calculate convergent 3-loop Feynman diagrams containing a single massive
loop equipped with twist $\tau =2$ local operator insertions corresponding to
spin $N$. They contribute to the massive operator matrix elements in QCD
describing the massive Wilson coefficients for deep-inelastic scattering at
large virtualities. Diagrams of this kind can be computed using an extended
version to the method of hyperlogarithms, originally being designed for
massless Feynman diagrams without operators. The method is applied to Benz- and
$V$-type graphs, belonging to the genuine 3-loop topologies. In case of the
$V$-type graphs with five massive propagators new types of nested sums and
iterated integrals emerge. The sums are given in terms of finite binomially and
inverse binomially weighted generalized cyclotomic sums, while the
1-dimensionally iterated integrals are based on a set of $\sim 30$ square-root
valued letters. We also derive the asymptotic representations of the nested
sums and present the solution for $N \in \mathbb{C}$. Integrals with a
power-like divergence in $N$--space $\propto a^N, a \in \mathbb{R}, a > 1,$ for
large values of $N$ emerge. They still possess a representation in $x$--space,
which is given in terms of root-valued iterated integrals in the present case.
The method of hyperlogarithms is also used to calculate higher moments for
crossed box graphs with different operator insertions.
