Optical excitation in a strongly neutral quasi-one-dimensional mixed-stack charge-transfer solid results in an exciton state, in which the electron and the hole are bound by electrostatic Coulomb interactions that are large, compared to the one-electron hopping. We present a joint theoretical-experimental demonstration of a new class of collective excitations, multiexcitons or exciton strings, consisting of a string of several (more than two) bound excitons, in a prototype neutral charge-transfer solid. The stability of the multiexciton states arise from the combined effects of one dimensionality and strong Coulomb interactions. Theoretically, we show that in narrow band one-dimensional semiconductors with long range Coulomb interactions, the occurrence of stable 2-exciton string (biexciton) necessarily implies stable higher multiexcitons. Experimentally, evidence for the multiexciton strings is demonstrated by femtosecond pump-probe spectroscopy of anthracene pyromellitic acid dianhydride. Excellent qualitative agreement is found between the calculated and the measured differential transmission spectra. Photoinduced absorptions to the 2-exciton string at low pump intensity and to the 3-exciton string at high pump intensity are observed, in agreement with the theory of excited state absorption. The 2-exciton string is confirmed also by a direct two-photon absorption measurement. The binding energies of the 2-exciton and the 3-exciton strings are obtained from the experimental data. The larger binding energy of the 3-exciton is in agreement with theory.