Two-dimensional (2D) metal-organic frameworks (MOFs) with a kagome lattice can exhibit strong electron-electron interactions, which can lead to tunable quantum phases including many exotic magnetic phases. While technological developments of 2D MOFs typically take advantage of substrates for growth, support, and electrical contacts, investigations often ignore substrates and their dramatic influence on electronic properties. Here, we show how substrates alter the correlated magnetic phases in kagome MOFs using systematic density functional theory and mean-field Hubbard calculations. We demonstrate that MOF-substrate coupling, MOF-substrate charge transfer, strain, and external electric fields are key variables, activating and deactivating magnetic phases in these materials. While we consider the example of kagome-arranged 9,10-dicyanoanthracene molecules coordinated with copper atoms, our findings should generalise to any 2D kagome material. This work offers useful predictions for tunable interaction-induced magnetism in surface-supported 2D (metal-)organic materials, opening the door to solid-state electronic and spintronic technologies based on such systems.