The strongly enhanced cooperative influence of medium polarity and organic structural design on the first hyperpolarizability beta of a novel family of highly polarizable azinium-(CH=CH-thienyl)-dicyanomethanido chromophores 1-3 is described. The dyes can be efficiently synthesized by regioselective protonation/alkylation of the corresponding bidentate anion precursors. Consecutive annelation of the pyridyl ring of 1 (pyridine-->quinoline-->acridine) and medium polarity effects are responsible for an extraordinarily variable range of intramolecular charge transfer (ICT), leading to a large set of pi-electron distribution patterns. Accordingly, systems with remarkably different zwitterionic/quinoid character in the ground and excited states present beta values in a broad range, eventually switching from negative to positive. Our investigation is based on a combination of experimental (UV/Vis spectroscopy, multinuclear NMR spectroscopy, and electrooptical absorption measurements) and computational (ab initio) approaches. It is shown that: 1) beta and mubeta are dramatically influenced, even by orders of magnitude, by a complex, non-monotonic interplay of structure and medium action, which in turn affects molecular ICT and bond length alternation (BLA), 2) the computations, validated by different experimental data, are to be recommended as an extremely useful tool in the search for a greatly improved set of molecular nonlinear optical (NLO) responses (in the case of 1-3 they show that such conditions may be attained only in a narrow and limited range of dielectric constants in which the annelation effect operates most efficiently), and 3) the search for the most favorable molecular NLO response of a highly polarizable chromophore both in solution and in solid matrices should simultaneously take into account not only the molecular design supplemented by annelation effects but also the polarity of the medium.