  We study the Riemann problem for the multidimensional compressible isentropic
Euler equations. Using the framework developed by Chiodaroli, De Lellis, Kreml
and based on the techniques of De Lellis and Sz\'{e}kelyhidi, we extend our
previous results and prove that whenever the initial Riemann data give rise to
a self-similar solution consisting of one admissible shock and one rarefaction
wave and are not too far from lying on a simple shock wave, the problem admits
also infinitely many admissible weak solutions.
