Attosecond Stimulated X-ray Raman Spectroscopy (SXRS) is a promising technique for investigating molecular electronic structure and photochemical processes with high spatial and temporal resolution. We present a theoretical study of SXRS from multiple core excitation sites of the same element. Two issues are addressed: interference between pathways contributing the signals from different sites; and how nuclear vibrations influence the signals. Taking furan as a model system, which contains two types of carbons Cα and Cβ, we performed time-dependent density functional theory calculations and computed the SXRS signals with two pulses tuned at the carbon K-edge. Our simulations demonstrate that the SXRS signal from the Cα and Cβ sites are non-additive, owing to the significant mixed contributions (Cα 1s excitations by the pump pulse followed by Cβ 1s excitations by the probe, or vice verse). Harmonic vibrations linearly coupled to the electronic transitions are incorporated using the cumulant expansion. The nuclei act as a bath for electronic transitions which accelerate the decay of time-domain signal. The frequency-domain spectrum is modified by a small red shift and high-resolution fine-structure features are introduced.