  In the Cardassian model, dark energy density arises from modifications to the
Friedmann equation, which becomes $H^2 = g(\rhom)$, where $g(\rhom)$ is a new
function of the energy density. The universe is flat, matter dominated, and
accelerating. The distance redshift relation predictions of generalized
Cardassian models can be very different from generic quintessence models, and
can be differentiated with data from upcoming pencil beam surveys of Type Ia
Supernovae such as SNAP. We have found the interesting result that, once
$\Omega_m$ is known to 10% accuracy, SNAP will be able to determine the sign of
the time dependence of the dark energy density. Knowledge of this sign (which
is related to the weak energy condition) will provide a first discrimination
between various cosmological models that fit the current observational data
(cosmological constant, quintessence, Cardassian expansion). Further, we have
performed Monte Carlo simulations to illustrate how well one can reproduce the
form of the dark energy density with SNAP.
  To be concrete we study a class of two parameter ($n$,$q$) generalized
Cardassian models that includes the original Cardassian model (parametrized by
$n$ only) as a special case. Examples are given of MP Cardassian models that
fit current supernovae and CMB data, and prospects for differentiating between
MP Cardassian and other models in future data are discussed. We also note that
some Cardassian models can satisfy the weak energy condition $w>-1$ even with a
dark energy component that has an effective equation of state $w_X < -1$.
