The acoustic interactions between gas bubbles in bubble plumes formed near the sea surface may significantly change the propagation and attenuation conditions for acoustical signals in the sea. The scattering properties of the bubble plumes have been studied extensively since Foldy's formulation of the theory for isotropic scattering by randomly distributed scatterers. This theory, modified later by others [K. W. Commander and A. Prosperetti, J. Acoust. Soc. Am. 85, 732--746 (1989)] fails in the vicinity of individual bubble resonances and for high concentrations of bubbles in the population. A recent improvement of the scattering theory [C. Feuillade, J. Acoust. Soc. Am. 98, 1178--1190 (1995)], predicts a downward frequency shift and a suppression of the attenuation peak. His results emphasize the importance of the still unsolved problem on proximity thresholds for influence of multiple scatteringin terms of bubble plume qualities. Available, but still unconfirmed, experimental data show the significance of multiple scattering in bubble plumes having void fractions >0.22%. This paper forms an attempt to illuminate and solve the proximity threshold question, forming the basis for the significance of contributions from multiple, linear scattering, by use of experimental data from laboratory and full-scale tests of bubble plume scattering.