We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint. In particular, for the pseudo-fermion limit of a large statistical angle θ ≈ π, we observe a wealth of exotic properties, including a first-order transition between different superfluid phases and a two-component partially paired phase for large fillings without need of an additional three-body hardcore constraint. In this limit, we analyze the effect of an induced hardcore constraint, which leads to the stabilization of superfluid ground states for vanishing or even small attractive onsite interactions. For finite statistical angles, we study the unconventional broken-symmetry superfluid peaked at a finite momentum, resulting in an interesting beat phenomenon of single-particle correlation functions. We show how some features of various ground-state phases, including an analog of the partially paired phase in the pseudo-fermion limit, may be reproduced in a naive mean field frame. © 2017 American Physical Society.