  Low-energy experiments allow for some of the most precise measurements in
particle physics, such as $g-2$. To make the most of these experiments, theory
needs to match the experimental precision. Over the last decade, this meant
that even in QED next-to-next-to-leading order calculations (or even more in
some cases) became necessary. McMule (Monte Carlo for MUons and other LEptons)
is a framework that we have developed to obtain NNLO predictions for a number
of processes, such as $e\mu \to e\mu$, $ee\to ee$, and $\mu\to e\nu\bar\nu$. I
will discuss some of the challenges faced when dealing with QED corrections and
some possible solutions we have implemented in McMule, namely the subtraction
scheme FKS$^\ell$, massification, and next-to-soft stabilisation. I will also
demonstrate how to calculate the three-loop massification constant that will be
required at N$^3$LO.
