  We present a loop-by-loop method for computing the differential equations of
Feynman integrals using the recently developed dual form formalism. We give
explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms.
Then, we test our formalism on a simple, but non-trivial, example: the two-loop
three-mass elliptic sunrise family of integrals. We obtain an epsilon-form
differential equation within the correct function space in a sequence of
relatively simple algebraic steps. In particular, none of these steps relies on
the analysis of $q$-series. Then, we discuss interesting properties satisfied
by our dual basis as well as its simple relation to the known epsilon-form
basis of Feynman integrands. The underlying K3-geometry of the three-loop
four-mass sunrise integral is also discussed. Finally, we speculate on how to
construct a "good" loop-by-loop basis at three-loop.
