  We introduce a phase space with spinorial momenta, corresponding to fermionic
derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is
a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on
this phase space with canonical equations equivalent to the Lagrangian
formulation, find the corresponding multisymplectic form and Hamiltonian
multivectors. The covariance of the formulation makes it possible to see how
additional non-manifest supersymmetries arise in analogy to those of the
Lagrangian formulation. We then observe that an intermediate phase space
Lagrangian defined on the sum of the tangent and cotanget spaces is a first
order Lagrangian for the sigma model and derive additional supersymmetries for
this.
