  We address the evolution of higher-order excited states, such as vortex and
multi-hump solitons, in nonlocal media with synthetic, competing focusing and
defocusing nonlinearities with different nonlocal transverse scales. We reveal
that introduction of suitable competing effects makes possible the
stabilization of vortex solitons with topological charge m>2, as well as
one-dimensional multi-hump solitons with number of humps p>4, all of which are
highly unstable in natural nonlocal materials with focusing nonlinearities.
