Isothermal titration calorimetry (ITC) is an apt tool for a total thermodynamic description of self-assembly of atypical amphiphiles such as anionic boron cluster compounds (COSAN) in water. Global fitting of ITC enthalpograms reveals remarkable features that differentiate COSAN from classical amphiphiles: (i) strong enthalpy and weak entropy contribution to the free energy of aggregation, (ii) low degree of counterion binding, and (iii) very low aggregation number, leading to deviations from the ideal closed association model. The counterion condensation obtained from the thermodynamic model was compared with the results of 7Li DOSY NMR of Li[COSAN] micelles, which allows direct tracking of Li cations. The basic thermodynamic study of COSAN alkaline salt aggregation was complemented by NMR and ITC experiments in dilute Li/NaCl and acetonitrile aqueous solutions of COSAN. The strong affinity of acetonitrile molecules to COSAN clusters was microscopically investigated by all-atomic molecular dynamics simulations. The impact of ionic strength on COSAN self-assembling was comparable to the behavior of classical amphiphiles, whereas even a small amount of acetonitrile cosolvent has a pronounced nonclassical character of COSAN aggregation. It demonstrates that large self-assembling changes are triggered by traces of organic solvents.