  Beauville introduced an integrable Hamiltonian system whose general level set
is isomorphic to the complement of the theta divisor in the Jacobian of the
spectral curve. This can be regarded as a generalization of the Mumford system.
In this article, we construct a variant of Beauville's system whose general
level set is isomorphic to the complement of the `intersection' of the
translations of the theta divisor in the Jacobian. A suitable subsystem of our
system can be regarded as a generalization of the even Mumford system
introduced by Vanhaecke.
