  (Abridged) The probability of detecting additional companions is essentially
unchanged with respect to the single-planet configurations, but after fitting
and subtraction of orbits with astrometric signal-to-noise ratio
$\alpha/\sigma_d\to 1$ the false detection rates can be enhanced by up to a
factor 2; the periodogram approach results in robust multiple-planet detection
for systems with periods shorter than the SIM mission length, even at low
values of $\alpha/\sigma_d$, while the least squares technique combined with
Fourier series expansions is arguably preferable in the long-period regime. The
accuracy on multiple-planet orbit reconstruction and mass determination suffers
a typical degradation of 30-40% with respect to single-planet solutions; mass
and orbital inclination can be measured to better than 10% for periods as short
as 0.1 yr, and for $\alpha/\sigma_d$ as low as $\sim 5$, while
$\alpha/\sigma_d\simeq 100$ is required in order to measure with similar
accuracy systems harboring objects with periods as long as three times the
mission duration. For systems with all components producing
$\alpha/\sigma_d\simeq 10$ or greater, quasi-coplanarity can be reliably
established with uncertainties of a few degrees, for periods in the range
$0.1\leq T\leq 15$ yr; in systems where at least one component has
$\alpha/\sigma_d\to 1$, coplanarity measurements are compromised, with typical
uncertainties on the mutual inclinations of order of $30^\circ-40^\circ$. Our
findings are illustrative of the importance of the contribution SIM will make
to the fields of formation and evolution of planetary systems.
