Two theoretical frameworks have been widely used to understand the response of monsoons to local and remote forcings: the vertically integrated atmospheric energy budget and convective quasi-equilibrium (CQE). Existing forms of these frameworks neglect some of the complexities of monsoons, such as the shallow meridional circulations that advect dry air from adjacent deserts into the middle and lower troposphere of monsoon regions. Here the fidelity of energy budget and CQE theories for monsoon location is assessed in a three-dimensional beta-plane model with boundary conditions representative of an off-equatorial continent with a tropical grassland and an adjacent subtropical desert. Energy budget theories show mixed success for various SST and land surface albedo forcings, with the ITCZ being collocated with the energy flux equator but a nonmonotonic relationship existing between ITCZ latitude and cross-equatorial energy transport. Accounting for the off-equatorial position of the unperturbed energy flux equator is shown to be important when a linearization of meridional energy transports is used to quantitatively diagnose ITCZ location. CQE theories that diagnose ITCZ location based on the subcloud moist static energy maximum are shown to have large biases; accounting for convective entrainment of dry air by using a lower-tropospheric mean moist static energy provides a more correct diagnosis of ITCZ location. Finally, it is shown that although ITCZ shifts can be diagnosed by modified CQE and energy budget frameworks, neither can be used in a quantitatively prognostic capacity because of unpredictable feedbacks that are often larger than the imposed forcing.