  We present the theoretical framework and the numerical setting of JASMINE2, a
code designed to efficiently solve the Jeans equations for multi-component
axisymmetric stellar systems. The models may include an arbitrary number of
stellar distributions, a dark matter halo, and a central supermassive black
hole; each stellar distribution is implicitly described by a two-integral
distribution function, and the stellar components can have different structural
(density profile, flattening, mass,scale-length), dynamical (rotation, velocity
dispersion anisotropy), and population (age, metallicity, initial mass
function, mass-to-light ratio) properties. In order to determine the ordered
rotational velocity and the azimuthal velocity dispersion fields of each
component, we introduce a decomposition that can be used when the commonly
adopted Satoh decomposition cannot be applied. The numerical implementation of
JASMINE2, and of the post-processing procedures (including projection), are
optimised to fully exploit the scalings allowed by the Poisson and the Jeans
equations. For illustrative purposes, we present three multi-component galaxy
models with a central black hole and a dark matter halo; one of the models is
also used to test JASMINE2 against available analytical solutions.
