Here is an example of a factorizing 3-loop integral that cannot be properly graphed
FCLoopIntegralToGraph[
SFAD[{{I*p1, 0}, {-m1^2, -1}, 1}]*
SFAD[{{I*(p2 - p3), 0}, {-m1^5, -1}, 1}]*
SFAD[{{I*(p3 + 0 q1), 0}, {-m1^2, -1}, 1}], {p1, p2, p3},
VertexDegree -> 8]
Essentially, we need a routine that can detect obviously factorizing integrals and then run FCLoopIntegralToGraph on
each integral separately.