Possess 1 -- possess the fly. The fly can be found in Room 11 at the same time the "lovely woman" is there.
Possess 2 -- possess the mouse. The mouse can be found under the heaters in the basement (go down from the storage room). You'll have to "fade" once after possessing the fly to move time along and get it to spawn.
Possess 3 -- possess the dog. It is in room 23 with the middle-aged woman in the same time period as the mouse first appears.

After that you'll be able to possess some humans. It works with at least Scott and Benjamin. Maybe others I haven't discovered yet.

Ending #1: Ghostbusters
Ending #2: Into heaven
Ending #3: Into hell
Ending #4: Spiritual Love Retreat
Ending #5: Creepy Hotel
Ending #6: From guest to hotel manager
Ending #7: Young Again
Ending #8: Black Hammer
Ending #9: Vengeance Served: The bitch is dead
Ending #10: I'm the Bitch Now
Ending #11: Vengeance Served: Killing the contender

#1: Read the bible (Spiritual achievement)
#2: Gazed at all the paintings (A day at the museum achievement)
#3: Spanked Ofelia after a spicy dinner (A false sense of achievement)
#4: Shagged to death by Valeriya (Murderous wife achievement)
#5: Read the old book (Studious ghost achievement)
#6: Tried to get a dime’s worth of soda (Living in the nineteen fifties achievement)
#7: Licked the nectar of a wild flower while flying by (Delectable guest achievement)
#8: Fucked a pillow doggy style (Lady with a dog achievement)
#9: Brought Ofelia to heaven (Italian Chef achievement)
#10: Ended a widow’s mourning (Asian maid achievement)
#11: Read the ledger every day (Master of time and space achievement)
#12: Spied on everyone (Voyeur extreme achievement)
#13: Proved to Alice that ghosts truly exist (Pretty receptionist achievement)
#14: Had fun with Valeriya for old time’s sake (Dazzling ex-wife achievement)
#15: Fucked Valeriya, Ofelia and Alice with the white vibrator (Forgotten tool achievement)
#16: Made love to Alice by borrowing her boyfriend’s tool (Naive girlfriend achievement)
#17: Came as Benjamin shoved his dick inside your rented cunt (Cheating boyfriend achievement)
#18: Fucked the shit out of Valeriya by commandeering Scott’s enormous cock (Russian bimbo achievement)
#19: Hammered by a monster black cock (Partner in crime achievement)
#20: Heard all virginity stories (Virginity fetish achievement)