FORTE 3 is an intermediate-resolution coupled atmosphere–ocean general circulation model (AOGCM) consisting of the Intermediate General Circulation Model 4 (IGCM4.1), a T42 spectral atmosphere with 35 <em>σ</em>-layers, coupled to Modular Ocean Model – Array (MOMA), a 2° × 2° ocean with 15 z-layer depth levels. It is a significant upgrade from its predecessor, the fast flexible AOGCM FORTE2, in terms of its mean climate and climate response. The model has been compiled using the Intel ifx compiler. Here we describe the changes between FORTE2 and FORTE3 and demonstrate its use by simulating global and Pacific ocean change under both idealised CO<sub>2</sub> forcing and stratospheric O<sub>3</sub> depletion. In the atmosphere a new formulation for convective entrainment in IGCM4.1 alleviates a cold upper tropospheric bias in IGCM4. The formulation for precipitating convection has been changed to reduce an existing strong negative cloud forcing bias in the model, and a new formulation for stratocumulus cloud has been introduced. Effects of changes are especially evidenced in climate simulations: the transient climate response in FORTE3 is 1.8 K, and the equilibrium climate sensitivity in a slab version of IGCM4.1 is 4.2 K, compared to FORTE2/slab IGCM4 values of 1.0 K and 2.1 K respectively, and are more consistent with CMIP6 GCMs and observations. In the ocean, a new parameterisation of equatorial mixing based on the meridional sea surface temperature gradient alleviates the equatorial cold bias. The Atlantic Meridional Overturning Circulation at 30° N is 17 Sv, while the transport of the Antarctic Circumpolar Current is 130 Sv, slightly stronger, and more in agreement in observations than FORTE2. We demonstrate the use of FORTE3 by conducting sensitivity experiments where CO<sub>2</sub> is increased by 1 % per year. We find that the introduction of a "high-volume" Andes mountain range does not change the pattern of global warming over the Pacific Ocean; conversely, the effect of stratospheric O<sub>3</sub> depletion does appear to change the equatorial Pacific gradient slightly.