  In superfluid dark matter (SFDM), the phonon field plays a double role: It
carries the superfluid's energy density and it mediates the MOND-like phonon
force. We show that these two roles are in tension with each other on galactic
scales: A MOND-like phonon force is in tension with a superfluid in equilibrium
and with a significant superfluid energy density. To avoid these tensions, we
propose a model where the two roles are split between two different fields.
This also allows us to solve a stability problem in a more elegant way than
standard SFDM. We argue that the standard estimates for the size of a galaxy's
superfluid core need to be revisited.
