  We extend our previous work on shot noise for entangled and spin polarized
electrons in a beam-splitter geometry with spin-orbit (\textit{s-o})
interaction in one of the incoming leads (lead 1). Besides accounting for both
the Dresselhaus and the Rashba spin-orbit terms, we present general formulas
for the shot noise of singlet and triplets states derived within the scattering
approach. We determine the full scattering matrix of the system for the case of
leads with \textit{two} orbital channels coupled via weak \textit{s-o}
interactions inducing channel anticrossings. We show that this interband
coupling coherently transfers electrons between the channels and gives rise to
an additional modulation angle -- dependent on both the Rashba and Dresselhaus
interaction strengths -- which allows for further independent coherent control
of the electrons traversing the incoming leads. We derive explicit shot noise
formulas for a variety of correlated pairs (e.g., Bell states) and lead spin
polarizations. Interestingly, the singlet and \textit{each} of the triplets
defined along the quantization axis perpendicular to lead 1 (with the local
\textit{s-o} interaction) and in the plane of the beam splitter display
distinctive shot noise for injection energies near the channel anticrossings;
hence, one can tell apart all the triplets, in addition to the singlet, through
noise measurements. We also find that spin-orbit induced backscattering within
lead 1 reduces the visibility of the noise oscillations, due to the additional
partition noise in this lead. Finally, we consider injection of two-particle
wavepackets into leads with multiple discrete states and find that two-particle
entanglement can still be observed via noise bunching and antibunching.
