  Dark matter (DM) simplified models are by now commonly used by the ATLAS and
CMS Collaborations to interpret searches for missing transverse energy
($E_T^\mathrm{miss}$). The coherent use of these models sharpened the LHC DM
search program, especially in the presentation of its results and their
comparison to DM direct-detection (DD) and indirect-detection (ID) experiments.
However, the community has been aware of the limitations of the DM simplified
models, in particular the lack of theoretical consistency of some of them and
their restricted phenomenology leading to the relevance of only a small subset
of $E_T^\mathrm{miss}$ signatures. This document from the LHC Dark Matter
Working Group identifies an example of a next-generation DM model, called
$\textrm{2HDM+a}$, that provides the simplest theoretically consistent
extension of the DM pseudoscalar simplified model. A comprehensive study of the
phenomenology of the $\textrm{2HDM+a}$ model is presented, including a
discussion of the rich and intricate pattern of mono-$X$ signatures and the
relevance of other DM as well as non-DM experiments. Based on our discussions,
a set of recommended scans are proposed to explore the parameter space of the
$\textrm{2HDM+a}$ model through LHC searches. The exclusion limits obtained
from the proposed scans can be consistently compared to the constraints on the
$\textrm{2HDM+a}$ model that derive from DD, ID and the DM relic density.
