  We implement an extension of the pseudofermion functional renormalization
group (PFFRG) method for quantum spin systems that takes into account two-loop
diagrammatic contributions. An efficient numerical treatment of the additional
terms is achieved within a nested graph construction which recombines different
one-loop interaction channels. In order to be fully self consistent with
respect to self-energy corrections we also include certain three-loop terms of
Katanin type. We first apply this formalism to the antiferromagnetic
$J_1$-$J_2$ Heisenberg model on the square lattice and benchmark our results
against the previous one-loop plus Katanin approach. Even though the RG
equations undergo significant modifications when including the two-loop terms,
the magnetic phase diagram -- comprising N\'eel ordered and collinear ordered
phases separated by a magnetically disordered regime -- remains remarkably
unchanged. Only the boundary position between the disordered and the collinear
phases is found to be moderately affected by two-loop terms. On the other hand,
critical RG scales, which we associate with critical temperatures $T_\text{c}$,
are reduced by a factor of $\sim2$ indicating that the two-loop diagrams play a
significant role in enforcing the Mermin-Wagner theorem. Improved estimates for
critical temperatures are also obtained for the Heisenberg ferromagnet on the
3D simple cubic lattice where errors in $T_\text{c}$ are reduced by $\sim34\%$.
