Multidimensional spectroscopy plays an important role in determining the dynamical and structural properties of chemical and biological systems. Exact quantum dynamical calculations for large complex systems are difficult. That opens the window for approximations to quantum dynamics to incorporate quantum effects in the calculation while having the computational difficulty similar to a classical mechanical calculation. Semiclassical approximations provide great alternatives to approximate quantum spectra. Optimized mean trajectory (OMT) approximation is one of such semiclassical approximations that was originally developed for the calculation of two dimensional infrared (2DIR) spectroscopy. Nonlinear response functions are the central theme to nonlinear spectra and in OMT approximation the response functions are expressed through an identification between a double sided Feynman diagram (DSD) and a semiclassical diagram whose evaluation only requires propagation of quantized classical trajectories. Here we have extended the OMT approach to the treatment of two dimensional electronic spectroscopy (2DES) for systems with multiple interacting discrete electronic states. The OMT approximation is further extended for relatively new mixed spectroscopic techniques, two dimensional electronic-vibrational (2DEV) spectroscopy and two dimensional vibrational-electronic (2DVE) spectroscopy. Another exact but alternative approach quantum mechanics, thermofield dynamics is examined for 2DES and 2DVE where we introduced OMT like semiclassical approximations. For all of these model the OMT is shown to nicely well with benchmark results.