The stimulated Brillouin scattering (SBS) is the main power limiting factor in the high-power narrow-line fiber laser circuits. A good way to increase the SBS power-threshold is to reduce its coherent gain, which is directly connected with the width of the Brillouin gain spectrum (BGS). The Brillouin gain peak and the phonons life-time are inversely proportional to the full-width-at-half-maximum of the BGS. The fine structure of the BGS and its ranges are sufficiently affected by parameters of the acoustic waveguide of the fiber. We propose a novel approach for increasing the BGS width and lowering its maximum (related directly to the SBS threshold) for a given optical refractive index profile. The aim of the approach is to maximize both the number and spectral spread of guided acoustic modes, as well as equate the acousto-optic interaction coefficients (acousto-optical overlap integrals) for the maximum possible number of these modes. This is due to the fact that an increase in the number of acoustic modes effectively contributing to the BGS, while preserving the distribution of the optical mode intensity, causes the scattered Stokes optical power to be redistributed accordingly between the corresponding number of Brillouin spectral lines, providing proportional damping of the Brillouin gain. Such an acoustically multimode SBS suppression can be achieved by tailoring a proper radial acoustic refractive index profile which can be fabricated by co-doping of silica with phosphorous oxide and fluorine.