They could bring in new ghosts in a number of ways I reckon. The house could host a fake seance to earn some money, but it accidentally brings back a ghost who has previously been "sucked off" or is stuck in purgatory.
Or perhaps a spirit could be trapped inside an object, like an ottoman or a chest. And when it's opened the ghost is in there. A chest would work for a pirate. Maybe a female pirate who's roughty toughty and worldly wise, but has 400+ years to catch up on after being trapped in the chest for so long. She could have been trapped in there using a voodoo curse, which is why she was able to be moved, but the curse was broken when the chest was opened. She could have a special ability to use some voodoo magic that she learnt on her travels to mess with guests.
Or they could accidentally dig up or release a ghost that's been trapped underground or in a wall cavity. Maybe they discover an old Roman mosaic in the garden and accidentally release the ghost of a Boudicca type figure.
Or the Button House Ripper who only appears every 10 years on the anniversary of his hanging. He was wrongly convicted and was pardoned but it was too late, the hangman had already started to pull the lever, and when he hung the rope snapped. So now he wonders a space between the living and the dead, with a noose around his neck, and can be seen one night a decade. However, Alison helps him access news of his pardon on Wikipedia and although it's not enough closure to get sucked off, it's enough to allow him permanent residence with the ghosts.