  Excited states (ESs) of two- and three-dimensional (2D and 3D) solitons of
the semivortex (SV) and mixed-mode (MM) types, supported by the interplay of
the spin-orbit coupling (SOC) and local nonlinearity in binary Bose-Einstein
condensates, are unstable, on the contrary to the stability of the SV and MM
solitons in their fundamental states. We propose a stabilization strategy for
these states in 3D, combining SOC and long-range Rydberg-Rydberg interactions
(RRI), in the presence of a spatially-periodic potential, that may include a
parity-time (PT)-symmetric component. ESs of the SV solitons, which carry
integer vorticities S and S+1 in their two components, exhibit robustness up to
S= 4. ESs of MM solitons feature an interwoven necklace-like structure, with
the components carrying opposite fractional values of the orbital angular
momentum. Regions of the effective stability of the 3D solitons of the SV and
MM types (both fundamental ones and ESs), are identified as functions of the
imaginary component of the PT-symmetric potential and strengths of the SOC and
RRI terms.
