Exciton management in organic light-emitting diodes (OLEDs) is vital for improving efficiency, reducing device aging, and creating new device architectures. In particular in white OLEDs, exothermic Förster-type exciton transfer, e.g. from blue to red emitters, plays a crucial role. It is known that a small exothermicity partially overcomes the spectral Stokes shift, enhancing the fraction of resonant donor-acceptor pair states and thus the Förster transfer rate. We demonstrate here a second enhancement mechanism, setting in when the exothermicity exceeds the Stokes shift: transfer to multiple higher-lying electronically excited states of the acceptor molecules. Using a recently developed computational method we evaluate the Förster transfer rate for 84 different donor–acceptor pairs of phosphorescent emitters. As a result of the enhancement the Förster radius tends to increase with increasing exothermicity, from around 1 nm to almost 4 nm. The enhancement becomes particularly strong when the excited states have a large spin-singlet character.