  The extended weight semigroup of a homogeneous space G/H of a connected
semisimple algebraic group G characterizes the spectra of the representations
of G on the spaces of regular sections of homogeneous linear bundles over G/H,
including the space of regular functions on G/H. We compute the extended weight
semigroups for all strictly irreducible affine spherical homogeneous spaces
G/H, where G is a simply connected non-simple semisimple complex algebraic
group and H a connected closed subgroup of it. In all the cases we also find
the highest weight functions corresponding to the indecomposable elements of
this semigroup. Among other things, our results complete the computation of the
weight semigroups for all strictly irreducible simply connected affine
spherical homogeneous spaces of semisimple complex algebraic groups.
