  Topological materials and their unusual transport properties are now at the
focus of modern experimental and theoretical research. Their topological
properties arise from the bandstructure determined by the atomic composition of
a material and as such are difficult to tune and naturally restricted to
$\leq3$ dimensions. Here we demonstrate that $n$-terminal Josephson junctions
with conventional superconductors may provide a straightforward realization of
tunable topological materials in $n-1$ dimensions. For $n\geq 4$, the Andreev
subgap spectrum of the junction can accommodate Weyl singularities in the space
of the $n-1$ independent superconducting phases, which play the role of
bandstructure quasimomenta. The presence of these Weyl singularities enables
topological transitions that are manifested experimentally as changes of the
quantized transconductance between two voltage-biased leads, the quantization
unit being $2e^2/(\pi\hbar)$.
