The structural evolution of andesitic melts with varying compositions remains one of the unsolved questions in high-temperature geochemistry and petrology. In this article, we report the structural details of model andesitic glasses [CaO–MgO–Na2O–Al2O3–SiO2 (CMNAS)] in the diopside (CaMgSi2O6) and jadeite (NaAlSi2O6) join using high-resolution, multi-nuclear, solid-state nuclear magnetic resonance (NMR). The 27Al NMR spectra of CMNAS glasses confirm that [4]Al is dominant. While a minor fraction of [5]Al is observed, its presence is only prevalent in the glasses with higher Ca–Mg content. Topological disorder in the glass network also tends to increase with Ca–Mg content as evidenced by the increase in the quadrupolar coupling constant (Cq) of [4]Al for glasses with increasing diopside contents (XDiopside). Despite the complex nature of the glasses studied here (with five oxide components), the 17O 3QMAS NMR spectra resolve diverse bridging oxygens (BOs) and non-bridging oxygens (NBOs), from which the degree of Al avoidance among framework cations (Si and Al) and preferential proximity among non-network cations (Ca2+, Mg2+, and Na+) and each oxygen site can be estimated: presence of Al–O–Al in jadeite glass implies a violation of the Al-avoidance rule in the glasses and the decrease in the fraction of NBOs with increasing XDiopside is consistent with a decrease in their viscosity. Analysis of the peak position of {Ca, Mg}-mixed NBOs, along with the absence of Na-NBO peak, and the peak shape of Si–O–Al reveals preferential partitioning of Ca2+ and Mg2 into NBOs and the proximity of Na+ to BOs. The fraction of highly coordinated Al has been linked to thermodynamic and transport properties of the melts. Considering all the experimental Al coordination environments available in the literature, together with the current experimental studies, we attempt to establish the relationship between the fractions of highly coordinated Al and composition, particularly average cationic potential of non-network forming cations (<c/r>ave, defined as cationic potential normalized by the mole fraction of each non-network cation). The fraction of highly coordinated Al increases nonlinearly with increasing <c/r>ave. The fraction of [5,6]Al is negligible up to <c/r>ave=∼1.7, then it increases above <c/r>ave>∼1.7 regardless of changes in other compositional variables (e.g., Si/Al, NBO content). This indicates the presence of a threshold <c/r>ave value for the formation of [5,6]Al. The current experimental results with the changes in network polymerization, coordination environments, and the degree of disorder in the CMNAS glasses can improve understanding of the structure–property (particularly, configurational thermodynamic properties) relationships of multi-component natural silicate melts, including andesitic melts and glasses.