  Even in the presence of conservation laws, one can perform arbitrary
transformations on a system if given access to a suitable reference frame,
since conserved quantities may be exchanged between the system and the frame.
Here we explore whether these quantities can be separated into different parts
of the reference frame, with each part acting as a `battery' for a distinct
quantity. For systems composed of spin-$\frac12$ particles, we show that the
components of angular momentum $S_x$, $S_y$ and $S_z$ (non-commuting conserved
quantities) may be separated in this way, and also provide several extensions
of this result. These results also play a key role in the quantum
thermodynamics of non-commuting conserved quantities.
