This work describes a resonance Raman study performed in domes of monolayer MoS2 using 23 different laser excitation energies covering the visible and near-infrared (NIR) ranges. The multiple-excitation results allowed us to investigate the exciton-phonon interactions of different phonons (A1’, E’ and LA) with different electronic and excitonic optical transitions in biaxially strained monolayer MoS2. The analysis of the intensities of the two first-order peaks, A1’ and E’, and the double-resonance 2LA Raman band as a function of the laser excitation furnished the values of the energies of the indirect gap and the excitonic transitions in the strained MoS2 domes. It was noticed that the out-of-plane A1’ phonon mode is significantly enhanced only by the indirect gap I and the C exciton, whereas the in-plane E’ mode is only enhanced by the C exciton of MoS2 dome, revealing thus a weak interaction of these phonons with the A and B excitons in the strained MoS2 domes. On the other hand, the 2LA Raman band is significantly enhanced at the indirect gap I transition and by the A (or B) exciton, but not enhanced by the C exciton, showing thus that the LA edge-phonons that participate in the double resonance process in MoS2 have a weak interaction with the C exciton.