Spatially varying B1 inhomogeneities and fat content are well known to be confounders of quantitative T1 mapping that use multi flip angle techniques. Separate B1 calibration maps can be acquired to correct flip angle errors cause by B1 inhomogeneities, but this requires an additional acquisition. In this work we consider an alternative approach that acquires variable flip angles and variable repetition times, and simultaneously estimates B1 inhomogeneity, T1, fat-fraction and R2*. The feasibility and noise performance of this approach are evaluated using theoretical Cramer-Rao Lower Bound analysis and simulations. Our results demonstrate that this approach is feasible, but suffers from relatively poor noise performance at typical acquisition parameters.