We analyze with our entropy-based Supermodel a library of 12 galaxy clusters featuring extended X-ray observations of their intracluster plasma (ICP). The few intrinsic parameters of the model—basically, the central level and the outer slope of the entropy profile—enable us to uniformly derive not only robust snapshots of the ICP thermal state, but also the "concentration" parameter marking the age of the host dark matter (DM) halo. We test these profiles for consistency with numerical simulations and observations. We find the central and the outer entropy correlate, so that these clusters split into two main classes defined on the basis of low (LE) or high entropy (HE) conditions prevailing throughout the ICP. We also find inverse correlations between the central/outer entropy and the halo concentration. We interpret these in terms of mapping the ICP progress on timescales around 5 Gyr toward higher concentrations, under the drive of the DM halo development. The progress proceeds from HE clusters to LE clusters, toward states of deeper entropy erosion by radiative cooling in the inner regions and of decreasing outer entropy production as the accretion peters out. We propose these radial and time features constitute a cluster Grand Design that we use here to derive a number of predictions. For HE clusters we predict sustained outer temperature profiles. For LEs we expect the outer entropy ramp to bend over; hence the temperature declines before steepening at low z; this feature goes together with an increasing turbulent support, a condition that can be directly probed with the Sunyaev-Zel'dovich effect. We finally discuss the looming out of two intermediate subsets: a wiggled {\widetilde{HE}} at low z that features central temperature profiles retaining imprints of entropy discharged by active galactic nuclei or deep mergers and high-z LEs where the cosmogony/cosmology had little time to enforce a sharp outer entropy bending.
