  In dimension $n=2$ and $3$, we show that for any initial datum belonging to a
dense subset of the energy space, there exist infinitely many global-in-time
admissible weak solutions to the isentropic Euler system whenever $1<\gamma\leq
1+\frac2n$. This result can be regarded as a compressible counterpart of the
one obtained by Szekelyhidi--Wiedemann (ARMA, 2012) for incompressible flows.
Similarly to the incompressible result, the admissibility condition is defined
in its integral form. Our result is based on a generalization of a key step of
the convex integration procedure. This generalization allows, even in the
compressible case, to convex integrate any smooth positive Reynolds stress. A
large family of subsolutions can then be considered. These subsolutions can be
generated, for instance, via regularization of any weak inviscid limit of an
associated compressible Navier--Stokes system with degenerate viscosities.
