  The power spectrum and voxel intensity distribution (VID) are two summary
statistics that can be applied to condense the information encoded in
line-intensity maps. The information contained in both summary statistics is
highly complementary, and their combination allows for a major increase in
precision of parameter estimation from line-intensity mapping (LIM) surveys.
Until recently, combination of these statistics required simulation-based
estimations of their covariance. In this work we leverage an analytical model
of covariance between these observables to run a joint Fisher forecast focusing
on the CO(1-0) rotational line targeted by the COMAP survey and a wider,
shallower hypothetical iteration. We consider a generalized phenomenological
non-CDM model, models with axion dark matter, and local primordial
non-Gaussianity, to highlight where a combined analysis of the power spectrum
and VID can be most useful. Our results demonstrate improvements in sensitivity
to beyond-$\Lambda$CDM physics over analyses using either the power spectrum or
VID on their own, by factors ranging from 2 to 50, showcasing the potential of
joint analyses in unlocking new insights into fundamental physics with LIM
surveys.
