Purpose: To develop a new sequence, MIMOSA, for highly-efficient T1, T2, T2*, proton density (PD), and source separation quantitative susceptibility mapping (QSM). Methods: MIMOSA was developed based on 3D-quantification using an interleaved Look-Locker acquisition sequence with T2 preparation pulse (3D-QALAS) by combining 3D turbo Fast Low Angle Shot (FLASH) and multi-echo gradient echo acquisition modules with a spiral-like Cartesian trajectory to facilitate highly-efficient acquisition. Simulations were performed to optimize the sequence. Multi-contrast/-slice zero-shot self-supervised learning algorithm was employed for reconstruction. The accuracy of quantitative mapping was assessed by comparing MIMOSA with 3D-QALAS and reference techniques in both ISMRM/NIST phantom and in-vivo experiments. MIMOSA's acceleration capability was assessed at R = 3.3, 6.5, and 11.8 in in-vivo experiments, with repeatability assessed through scan-rescan studies. Beyond the 3T experiments, mesoscale quantitative mapping was performed at 750 um isotropic resolution at 7T. Results: Simulations demonstrated that MIMOSA achieved improved parameter estimation accuracy compared to 3D-QALAS. Phantom experiments indicated that MIMOSA exhibited better agreement with the reference techniques than 3D-QALAS. In-vivo experiments demonstrated that an acceleration factor of up to R = 11.8-fold can be achieved while preserving parameter estimation accuracy, with intra-class correlation coefficients of 0.998 (T1), 0.973 (T2), 0.947 (T2*), 0.992 (QSM), 0.987 (paramagnetic susceptibility), and 0.977 (diamagnetic susceptibility) in scan-rescan studies. Whole-brain T1, T2, T2*, PD, source separation QSM were obtained with 1 mm isotropic resolution in 3 min at 3T and 750 um isotropic resolution in 13 min at 7T. Conclusion: MIMOSA demonstrated potential for highly-efficient multi-parametric mapping.