Multi-parameter mapping (MPM) magnetic resonance imaging (MRI) provides quantitative estimates of the longitudinal and effective transverse relaxation rates R1 and R2*, proton density (PD), and magnetization transfer saturation (MTsat). Thereby, MPM enables better comparability across sites and time than conventional weighted MRI. However, for MPM, several contrasts must be acquired, resulting in prolonged measurement durations and thus preventing MPM's application in clinical routines. State-of-the-art imaging acceleration techniques such as Compressed SENSE (CS), a combination of compressed sensing and sensitivity encoding, can be used to reduce the scan time of MPM. However, the accuracy and precision of the resulting quantitative parameter maps have not been systematically evaluated. In this study, we therefore investigated the effect of CS acceleration on the fidelity and reproducibility of MPM acquisitions. In five healthy volunteers and in a phantom, we compared MPM metrics acquired without imaging acceleration, with the standard acceleration (SENSE factor 2.5), and with Compressed SENSE with acceleration factors 4 and 6 using a 32-channel head coil. We evaluated the reproducibility and repeatability of accelerated MPM using data from three scan sessions in gray and white matter volumes-of-interest (VOIs). Accelerated MPM provided precise and accurate quantitative parameter maps. For most parameters, the results of the CS-accelerated protocols correlated more strongly with the non-accelerated protocol than the standard SENSE-accelerated protocols. Furthermore, for most VOIs and contrasts, coefficients of variation were lower when calculated from data acquired with different imaging accelerations within a single scan session than from data acquired in different scan sessions with the same acceleration method. These results suggest that MPM with Compressed SENSE acceleration factors up to at least 6 yields reproducible quantitative parameter maps that are highly comparable to those acquired without imaging acceleration. Compressed SENSE can thus be used to considerably reduce the scan duration of R1, R2*, PD, and MTsat mapping, and is highly promising for clinical applications of MPM.