Femtosecond Stimulated Raman Spectroscopy (FSRS) is motivated by the knowledge of the molecular geometry changes that accompany sub-picosecond chemical reactions. The detection of vibrational resonances throughout the entire fingerprint region of the spectrum with sub-100-fs delay precision is fairly straightforward to accomplish with the FSRS technique. Despite its utility, FSRS must contend with substantial technical challenges that stem from a large background of residual laser light and lower-order nonlinearities when all laser pulses are electronically resonant with the equilibrium system. In this work, a geometry based on five incident laser beams is used to eliminate much of this undesired background in experiments conducted on metmyoglobin. Compared to a three-beam FSRS geometry with all electronically resonant laser pulses, the five-beam approach described here offers major improvements in the data acquisition rate, sensitivity, and background suppression. The susceptibility of the five-beam geometry to experimental artifacts is investigated using control experiments and model calculations. Of particular concern are undesired cascades of third-order nonlinearities, which are known to challenge FSRS measurements carried out on electronically off-resonant systems. It is generally understood that "forbidden" steps in the desired nonlinear optical processes are the origin of the problems encountered under off-resonant conditions. In contrast, the present experiments are carried out under electronically resonant conditions, where such unfortunate selection rules do not apply. Nonetheless, control experiments based on spectroscopic line shapes, signal phases, and sample concentrations are conducted to rule out significant contributions from cascades of third-order processes. Theoretical calculations are further used to estimate the relative intensities of the direct and cascaded responses. Overall, the control experiments and model calculations presented in this work suggest promise for multidimensional resonance Raman investigations of heme proteins.