We perform theoretical studies of nonlinear spectral responses of molecular aggregates upon multiple electronic excitations. It is shown that the transient absorption (TA) spectra exhibit gradual shifting to short wavelengths upon an increase in excitation energy accompanied by population of higher-order exciton manifolds. This transformation of the TA profile reflects a character of the exciton splitting and, therefore, is strongly dependent on the aggregate shape and size as well as on the exciton couplings and disorder of the site energies. The theory is applied for modeling of the intensity-dependent TA spectra of a light-harvesting LH1 antenna from a photosynthetic purple bacterium. Fitting of the data allowed verification of the exciton model of the complex (enabling us to differentiate between the correlated (elliptical) and uncorrelated energetic disorder). We found that the difference between the TA spectra corresponding to the absorption of one and two quanta suggests the presence of strong uncorrelated disorder (in agreement with earlier models of bacterial LH1/LH2 antennas). Nonlinear spectroscopy with multiple excitations may also be useful for exploring the exciton structure of other photosynthetic antennas and similar molecular systems.