  The large-scale mass distributions of galaxy-scale strong lenses have long
been assumed to be well-described by a singular ellipsoidal power-law density
profile with external shear. However, the inflexibility of this model could
lead to systematic errors in astrophysical parameters inferred with
gravitational lensing observables. Here, we present observations with the
Atacama Large (sub-)Millimetre Array (ALMA) of three strongly lensed dusty
star-forming galaxies at $\simeq30$ mas angular resolution and investigate the
sensitivity of these data to angular structure in the lensing galaxies. We
jointly infer the lensing mass distribution and the full surface brightness of
the lensed sources with multipole expansions of the power-law density profile
up to fourth order using a technique developed for interferometric data. All
three data sets strongly favour third and fourth-order multipole amplitudes of
$\approx1$ percent of the convergence. While the infrared stellar isophotes and
isodensity shapes agree for one lens system, for the other two the isophotes
disagree to varying extents, suggesting contributions to the angular structure
from dark matter intrinsic or extrinsic to the lensing galaxy.
