  In usual superconductivity (SC), the pairs have zero total momentum
irrespective of their symmetry. Staggered SC would involve, instead, pairs with
a finite commensurate total momentum, but such exotic states have never been
proven to be realized in nature. Here we study for the first time the influence
of particle-hole asymmetry on the competition of staggered SC with Charge
Density Waves (CDW) in a ferromagnetic medium. We obtain unprecedented
situations in which CDW and staggered SC coexist. We also obtain cases of a SC
dome near the collapse of a CDW state as well as cascades of transitions that
exhibit remarkable similarities with the pressure phase diagram in UGe$_2$
suggesting that SC in this material may be staggered coexisting and competing
with a CDW state.
