We performed an agnostic search in the data from the first three observing runs of LIGO - Advanced LIGO and Virgo - Advanced Virgo for a novel model of stochastic gravitational waves background (SGWB). The SGWB power spectrum is produced, in this case, by a superposition of the stochastic compact binary coalescence signals (CBCs) and a double-peaked gravitational waves domain wall model. The two peaks were characterized using broken power-law models. We placed a $95\%$ confidence level upper limits on the gravitational wave energy density at $25 Hz$ from CBCs and, simultaneously, on the amplitude of the two peaks. Detection prospects using these upper limit values are discussed for third generation detectors, such as the Einstein Telescope.