  A Thouless pump transports an integer amount of charge when pumping
adiabatically around a singularity. We study the splitting of such a critical
point into two separate critical points by adding a Hubbard interaction.
Furthermore, we consider extensions to a spinful Rice-Mele model, namely a
staggered magnetic field or an Ising-type spin coupling, further reducing the
spin symmetry. The resulting models additionally allow for the transport of a
single charge in a two-component system of spinful fermions, whereas in the
absence of interactions, zero or two charges are pumped. In the SU(2)-symmetric
case, the ionic Hubbard model is visited once along pump cycles that enclose a
single singularity. Adding a staggered magnetic field additionally transports
an integer amount of spin while the Ising term realizes a pure charge pump. We
employ real-time simulations in finite and infinite systems to calculate the
adiabatic charge and spin transport, complemented by the analysis of gaps and
the many-body polarization to confirm the adiabatic nature of the pump. The
resulting charge pumps are expected to be measurable in finite-pumping speed
experiments in ultra-cold atomic gases, for which the SU(2) invariant version
is the most promising path. We discuss the implications of our results for a
related quantum-gas experiment by Walter et al. [arXiv:2204.06561].
