We use the harmonic superposition approach to examine how a single atom substitution affects low-temperature anomalies in the vibrational heat capacity (C) of model nanoclusters. Each anomaly is linked to competing solidlike "phases", where crossover of the corresponding free energies defines a solid-solid transition temperature (T). For selected Lennard-Jones clusters we show that T and the corresponding CV peak can be tuned over a wide range by varying the relative atomic size and binding strength of the impurity, but excessive atom-size mismatch can destroy a transition and may produce another. In some tunable cases we find up to two additional C peaks emerging below Ts, signalling one- or two-step delocalisation of the impurity within the ground-state geometry. Results for Ni$\mathrm{<mrow\; data-mjx-texclass="ORD">74</mrow>}$X and Au$\mathrm{<mrow\; data-mjx-texclass="ORD">54</mrow>}$X clusters (X = Au, Ag, Al, Cu, Ni, Pd, Pt, Pb), modelled by the many-body Gupta potential, further corroborate the possibility of tuning, engineering, and suppressing finite-system analogues of a solid-solid transition in nanoalloys.