Magnetic resonance fingerprinting is an MRI-based technique that allows for fast, simultaneous quantitative mapping of multiple tissue parameters. Multi-component MRF (MC-MRF) additionally allows for the mapping of multiple tissue components per voxel. Currently, most MC-MRF implementations ignore any nonlinear effects on signals resulting from multi-component systems, such as the effects introduced by magnetisation transfer (MT). Here, we investigate the effects of free pool to free pool magnetisation transfer on the accuracy of MC-MRF, with a focus on the application of this technique for myelin water fraction (MWF) imaging. Assessment of the different MC-MRF techniques is done through application of these algorithms to two-component numerical phantoms, where the signals from two interacting components were simulated using the EPG-X framework. Results show that MT has a negative effect on the accuracy of the acquired parameter estimates for all estimated parameters, resulting in biases and incorrect parameter estimates. Several adjusted methods for MC-MRF including magnetisation transfer were proposed and tested. Although theoretically improvements were expected, the used sequences showed to be inadequate for accurate MT estimates. More research into these techniques is still required to improve their performance and accuracy. A technique left mainly unexplored here is sequence optimisation to minimise the effects of magnetisation transfer on the resulting signals. A quick exploration, however, showed that this might be a viable approach for future research as well.