Structural, magnetization and heat capacity studies were performed on Ce$_2$(Pd$_{1-x}$Ni$_x$)$_2$Sn ($0 \leq x \leq 1$) alloys. The substitution of Pd atoms by isoelectronic Ni leads to a change in the crystallographic structure from tetragonal (for $x \leq 0.3$) to centered orthorhombic lattice (for $x \geq 0.4$). The volume contraction thorough the series is comparable to the expected from the atomic size ratio between transition metal components. The consequent weak increase of the Kondo temperature drives the two transitions observed in Ce$_2$Pd$_2$Sn to merge at $x = 0.25$. After about a 1% of volume collapse at the structural modification, the system behaves as a weakly magnetic heavy fermion with an enhanced degenerate ground state. Notably, an incipient magnetic transition arises on the Ni-rich size. This unexpected behavior is discussed in terms of an enhancement of the density of states driven by the increase of the $4f$-conduction band hybridization and the incipient contribution of the first excited crystal field doublet on the ground state properties.