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We present results of magnetic susceptibility and thermal expansionmeasurements performed on high-quality single crystals ofEuPd$_2$(Si$_{1-x}$Ge$_x$)$_2$ for 0 $\leq$ x $\leq$ 0.2 and temperatures 2 K$\leq T \leq$ 300 K. Data were taken at ambient pressure and finite He-gaspressure $p$ $\leq$ 0.5 GPa. For x = 0 and ambient pressure we observe apronounced valence-change crossover centred around $T'_V$ $\approx$ 160 K witha non-magnetic ground state. This valence-change crossover is characterized byan extraordinarily strong pressure dependence of d$T'_V$ /d$p$ = (80 $\pm 10)$K/GPa. We observe a shift of $T'_V$ to lower temperatures with increasingGe-concentration, reaching $T'_V$ $\approx$ 90 K for x = 0.1, while stillshowing a non-magnetic ground state. Remarkably, on further increasing x to 0.2we find a stable Eu$^{(2+\delta)+}$ valence with long-range antiferromagneticorder below $T_N$ = (47.5 $\pm$ 0.1) K, reflecting a close competition betweentwo energy scales in this system. In fact, by the application of hydrostaticpressure as small as 0.1 GPa, the ground state of this system can be changedfrom long-range antiferromagnetic order for $p$ $<$ 0.1 GPa to anintermediate-valence state for $p$ $\geq$ 0.1 GPa.

From magnetic order to valence-change crossover in EuPd$_2$(Si$_{1-x}$Ge$_x$)$_2$ using He-gas pressure